Chen was grazed in the stomach while Vice President Annette Lu was hit in the right knee. Their wounds were not life-threatening, said Chiou I-jen, secretary-general in the Presidential Office.
There was no immediate report of arrests, and the motive for the apparent assassination attempt in a street choked with Chens supporters in the southern city of Tainan was unclear.
Doctors showed pictures of a 4.4-inch wound just under Chens navel.
The economic ripple effect of the attack on Chen and Lu shook the Asia-Pacific, dragging down currencies in the region including the peso, which closed at a new historic low of 56.38 to the dollar after trading at a high of 56.26.
Market sources said the weakness in the regional currencies that resulted from the Taiwan incident immediately created pressure on the peso.
Meanwhile, President Arroyo expressed her official well wishes and prayers for the conduct of "safe and orderly" elections in Taiwan today.
In a brief statement issued from the Palace, Mrs. Arroyo said she was "sorry" to hear about the shooting of Chen and Lu and she welcomed the news that "their injuries were not life-threatening and that they have been declared out of danger by attending (physicians)."
"I hope the political exercise in Taiwan... will proceed in a safe and orderly manner," she added. Mrs. Arroyo issued this statement even as the Philippines maintains a "one-China" policy, which recognizes Chinas stance that Taiwan is a renegade province.
Chan Chi-hsien, head of Chi Mei Hospital where Chen was being treated, said the bullet didnt go deep into the presidents body, and there was no injury to internal organs.
After the shooting, the president "was very conscious and he walked into our emergency room," Chan said.
There was no immediate public reaction to the shooting from China.
Taiwans presidential vote will go ahead as planned today, an election official said. Campaign rallies, however, have been canceled.
A large crowd of Chen supporters gathered outside the hospital in Tainan. Using Chens nickname, the crowd chanted, "A-bian, get elected," as they pumped their arms in the air. Some waved green flags, the color of Chens Democratic Progressive Party.
Chen was riding in a red convertible four-wheel-drive vehicle and waving to crowds lining the streets in his hometown. People were setting off celebratory fireworks as he drove by and early media reports said he was injured by firecrackers.
"The vice president first felt pain in her knee and she thought it was caused by firecrackers," Chiou said. "Then the president felt some wetness on his stomach area, and then they realized something was wrong."
Hospital head Chan said the bullet grazed the vice presidents right knee, leaving a wound about two centimeters. The bullet caused no bone fractures and it wasnt found, he said.
Opposition candidate Lien Chan told a news conference, "We were very, very shocked. We wish President Chen and Vice President Lu will recover soon. We strongly condemn any form of violence."
Officials have declined to speculate about who fired the shots.
This is the first time a Taiwanese president has been shot, though Chen insists that his wife, Wu Shu-chen, was the target of an assassination attempt in 1985 when a truck ran over her three times, leaving her paralyzed from the waist down.
Chen has accused the Nationalist Party of being involved, but the truck driver and party insisted it was an accident and the driver wasnt charged.
As a grassroots politician, Chen enjoys street campaigning and frequently wades into big crowds. Security is relatively relaxed because theres not a tradition of violence against leaders.
This election has been an emotional, hotly contested race dominated by negative campaigning. Lien is promising to take a softer approach with the islands biggest rival, China.
Philip Yang, a political scientist at National Taiwan University in Taipei, said that it was too early to say how the shooting could affect the election results.
"It could bring out sympathy votes" for the president, Yang said. "Or it could consolidate the blue camp," he added, referring the opposition Nationalist Party.
China did not immediately comment on Fridays shooting. Its Foreign Ministry referred questions to the Cabinets Taiwan Affairs Office, which did not answer telephone calls.
In the months leading up to the election, China harshly criticized Chen. It also bitterly denounced an unprecedented island-wide referendum, spearheaded by Chen, that will ask Taiwanese voters whether the island should beef up its defenses against hundreds of Chinese missiles pointed at it. China, which claims Taiwan is part of its territory and insists the two should be unified, fears the referendum could lead to a future vote on Taiwanese independence.
"Some people in the Taiwan authorities have been trying to push for a referendum on Taiwan independence based on the pretense of democracy," Chinese Premier Wen Jiabao said in a news conference earlier this week. "They have undermined this universally recognized principle of one China and threatened stability in the Taiwan Strait."
China and Taiwan split when the Communists took over the mainland in 1949, and Beijing is pressuring Taiwan to unify.
Lien and Chen agree on most basic issues involving China policy. Neither candidate favors immediate unification, and both are highly distrustful of the Communist leadership.
However, Chen has been more aggressive in pushing for a Taiwanese identity separate from Chinas, and this has raised tensions with Beijing. China has threatened to attack if Taiwan seeks a permanent split. Marichu Villanueva