Jackson suffered complications related to recent gall bladder surgery and was in the base hospital.
Al Jazeera's Monica Villamizar, reporting from Guantanamo Bay, said that a dramatic situation unfolded when Jackson fainted.
"He was taken out of the building and onto a stretcher. We really don't know what his condition is, and it is still unclear whether the trial will resume tomorrow."
Toronto-born Khadr was 15 when captured during a gunfight at an al-Qaeda compound in Afghanistan in 2002.
He is the first person since World War Two to face trial in a military tribunal for acts allegedly committed as a minor.
The United Nations said earlier this week that the trial at the Guantanamo Bay naval base was of dubious legality and could set a dangerous precedent for child soldiers worldwide.
Now 23-years-old, Khadr is accused of killing a US soldier with a grenade during the battle and making roadside bombs to target US troops.
Prosecutor Jeff Groharing said Khadr was raised in a family of "Islamist extremists" who spent holidays with Osama bin Laden, trained their son to use bombs and guns and encouraged him to kill Americans.
"I am a terrorist trained by al-Qaeda -- those are Omar Khadr's own words," Groharing told the seven military officers on the jury.
"Those words were confirmed by his acts."
He said Khadr described in detail pulling the pin of a grenade and lobbing it over his shoulder at US special forces who entered the mud-walled compound.
However, Jackson said Khadr was in the compound with three "bad men" and that one of them threw the grenade that killed the soldier before being fatally shot himself by the US troops.
"Omar Khadr did not kill Sergeant Speer. He has been waiting eight long years to tell you that. To tell somebody who can finally listen and who can finally make a difference," Jackson told the jury.
Khadr was in the compound only because his father, Ahmed Khadr, took him there to translate for the bomb-makers, he said.
Khadr's case is the first to go to trial under the system of military commissions for detainees captured by US forces in a global campaign following the September 11, 2001, attacks on the US.
Obama had sought to close the detention centre that has been the object of international condemnation, but he has faced congressional opposition on transferring the detainees to US soil.
The president has introduced some changes designed to extend more legal protections to detainees, but the tribunals' long-term future remains uncertain.