The Did You Hear About the Morgans? actor allegedly refused to call an ambulance as he "didn't want to waste paramedics' time" and waited for hours at the Chelsea and Westminster Hospital without "making any fuss".
A source told The Sun: "You'd have had no idea he was a huge star."
The 50-year-old apparently returned home after he was discharged later that night, although his spokesperson has refused to comment.
Grant recently praised the work of medical staff in the UK as his role as ambassador for cancer charity Marie Curie. His mother died of pancreatic cancer in 2001.
The About a Boy star said at the time: "The nurses were just fantastic, whether the normal NHS (National Health Service) nurses or the Marie Curie nurses whose entire life is spent sitting in the dark with someone who is dying.
"They almost earn nothing, but if I put them next to my hedge fund friends I know who is happier."