Lord Prescott, 81, was taken to hospital in Hull on Friday, his family said in a statement.
"We would like to praise the swift actions of the ambulance staff and the doctors and nurses at Hull Royal Infirmary's A&E and stroke unit," the statement said.
"They have been remarkable and we cannot thank them enough.
"He is receiving excellent care from the NHS but we would respectfully request at this time that John and our family are given the privacy we need so that he can have the time and space to make a full recovery."
A former trade union activist, John Prescott served for ten years as Tony Blair's deputy prime minister following Labour's 1997 general election landslide.
During much of that time, he acted as a conciliator in the often turbulent relationship between Mr Blair and chancellor Gordon Brown.
While a loyal supporter of Mr Blair in office, in more recent years he has been critical of elements of New Labour's legacy denouncing Britain's involvement in the Iraq War.
He has strongly defended Jeremy Corbyn in the face of fierce criticism by other figures from the New Labour era.