The Bryan twins, who were seeded No. 1, have now failed to reach the final at any of the last three Grand Slam tournaments -- after winning four major titles in a row before that, starting at the 2012 US Open.
Their bid for the first calendar-year Grand Slam in men's doubles since 1951 ended with a semifinal loss at last year's US Open. The Bryans then lost in the third round at the Australian Open in January.
"Obviously, we're disappointed," Mike said. "We thought we could have played a little better."
The brothers own a record 15 major doubles championships, including at Roland Garros in 2003 and 2013.
The Associated Press contributed to this report.