Uribe will continue to work from home for about a week while he recovers, Velasquez said.
Dr Alberto Cortez, an infectious disease specialist at Colombia's Universidad Nacional, warned it was possible that the disease could have been passed to others attending the summit.
But he said it needed to be established when Uribe became sick to determine whether he picked up the virus in Argentina, where many cases of the disease have been reported, or if he arrived with it.
Hugo Chavez, the Venezuelan president, said he had felt fine after returning from Argentina and did not see any need to be tested.
"I regret this and hope there are no repercussions for the president's health and that nobody else has caught the disease"
"At this moment, no, because I do not have anything," Chavez said. "I am so well that last night I pitched [in a game of softball]".
The Union of South American Nations summit was called after a number of nations, including Venezuela, criticised Colombia for agreeing to allow more US troops to be deployed at the country's military bases.
Chavez has threatened to cut ties with Bogota over the issue, but on Sunday he wished his Colombian counterpart a speedy recovery.
"I regret this and hope there are no repercussions for the president's health and that nobody else has caught the disease," he said.
Uribe is the second Latin American leader to come down with H1N1 after Oscar Arias, the Costa Rican president, announced on August 11 that he had the virus and was being quarantined at his home.
Colombia has reported 621 confirmed cases of swine flu, including Uribe's.
There have been 34 deaths from the illness, according to the social protection ministry.
The virus has spread widely since emerging in April in Mexico and the United States.
The World Health Organistation declared a pandemic in June.