Having qualified for the finals of the rings event on Saturday, Van Gelder spent the night celebrating and returned in the early hours of Sunday.
The Dutch team said the 33-year-old violated rules concerning alcohol consumption and leaving the team base.
In 2009, Van Gelder was suspended after taking cocaine three days before the national championships.
"It's terrible for Yuri, but this kind of behaviour is unacceptable," said Dutch team chef de mission Maurits Hendriks in a statement.
"In sports terms this is a disaster, but we had no other choice given the violation of our values."
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Dutch gymnast Yuri van Gelder has been sent home from the Olympics after drinking alcohol on a night out in Rio.