The politician, who declared a hunger strike on October 1, was arrested after returning to Georgia, having lived abroad for years.
He faces up to six years in jail after being convicted in absentia in 2018 of abuse of power and concealing evidence when he was president, charges he rejects as politically motivated.
"One of the parameters of Saakashvili's blood test was bad, so local prison doctors and an emergency ambulance team helped me with the transfusion and after that Saakashvili's condition stabilised," Nikoloz Kipshidze, Saakashvili's doctor, was quoted as saying by Interfax.
Kipshidze believes that Saakashvili should be transferred to a city hospital because "the crisis can recur and it would be difficult to cope with it in a prison hospital," Interfax added.
The 53-year-old Saakashvili led the Rose Revolution in 2003 that ousted veteran leader Eduard Shevardnadze. Saakashvili ruled as president from 2004 to 2013 before leaving the country and building a new political career in Ukraine.
He was arrested and jailed on October 1 after returning home on the eve of parliamentary elections to rally the opposition and "take part in saving Georgia".
Last week thousands of his supporters rallied in the capital Tbilisi to demand his release.