Coach John Fox said it was for "personal reasons," and he expected Jennings to return Friday.
Jennings is coming off a subpar 2014 campaign in which he contributed 50 tackles in 16 starts with seven pass breakups and one forced fumble.
The team signed Jennings to a four-year, $22.4 million extension in January 2014. Former general manager Phil Emery said the deal was "rewarding excellence" for a veteran who took on the responsibilities in 2013 as a No. 1 cornerback after Charles Tillman suffered a season-ending injury.
Jennings' deal was worth $11.8 million guaranteed and included a $3 million signing bonus.
ESPN Bears reporter Jeff Dickerson contributed to this report.