The 67-year-old professor, who has motor neuron disease, is "comfortable" at Addenbrooke's Hospital in Cambridge, his employers said.
He was described as "very ill" when he was admitted to the hospital on Monday with a suspected respiratory infection.
The author of A Brief History of Time has been unwell for weeks.
A Cambridge University spokesman said: "Professor Hawking is being kept in for observation at Addenbrooke's Hospital... he is comfortable and his family is looking forward to him making a full recovery."
The physicist, who uses a wheelchair and speaks using a voice synthesizer, has worked at Cambridge University for more than 30 years.
Curtailed US trip
He had flown at the end of February to the California Institute of Technology where he is a visiting scholar.
But he called off an appearance at Arizona State University on 6 April because of his illness and flew back to the UK last Saturday.
Prof Hawking developed symptoms of motor neuron disease while studying in the 1960s and is one of the world's longest-surviving sufferers.
The scientist has three children and one grandchild. He became a CBE in 1982 and a Companion of Honor in 1989.
Last year, it was announced he would be stepping down as the university's Lucasian Professor of Mathematics at the end of this academic year.
It is policy for holders of the title to retire at 67, but Prof Hawking said he intended to continue working as Emeritus Lucasian Professor of Mathematics.