The 63-year-old, who has been in charge at Villa Park since September, was in a "comfortable condition" but will remain in hospital for several days after having tests, the club said on their official website.
Thursday's training was being taken by his assistant Gary McAllister and Houllier will not be at Saturday's league match against Stoke City at Villa Park.
Villa chief executive Paul Faulkner said: "I spoke with him (Houllier) this morning, as did Gary before he took training, and he sounded very positive.
"I've also received a lot of good wishes from fans and would like to thank them for their kind thoughts in wishing Gerard a speedy recovery."
Houllier's compatriot, UEFA President Michel Platini, said after a news conference promoting the 2016 European Championship: "Our thoughts are with Gerard, we wish him well."
