Edward, 77, was taken to University College in London after becoming ill Sunday night and was later transferred to King Edward VII Hospital, The Daily Telegraph reported.
The palace characterized the stroke as "mild." Edward has reportedly been able to speak to hospital staff.
The duke was expected to stay in the hospital "a few more days" before going home, a spokesman for the duke said.
He has canceled all engagements for the next three weeks.
Edward is president of the Stroke Association.