"I don't know how long he's going to be gone," Oakland manager Bob Geren said of Braden before the start of a three-game series against the host Red Sox at Fenway Park. "It's a family thing, and we'd rather keep that private. ... We'll miss him and we're praying for him."
A player is allowed to spend no more than seven days on bereavement leave.
Braden, who has the lowest ERA (3.13) among A's starting pitchers, was scheduled to make his 18th start of the season Tuesday. It has not been announced who will replace him in the rotation, but Eveland is the logical candidate.
Optioned to Sacramento on May 5 after going 1-2 with a 7.40 ERA in six games (five starts) to open the season, Eveland, 25, would be working on three days of rest Tuesday.
Another option is righty Edgar Gonzalez, who has worked mostly in a long-relief role and last appeared Friday in Cleveland, allowing one hit in an inning of work. Gonzalez, 26, is 0-1 with a 5.40 ERA in two starts for the A's this year.
"I want to talk to Dana and see how he feels before we make any decisions," Geren said of Eveland, who was 7-1 with a 3.49 ERA in 12 starts at Sacramento.
Geren said Monday's game would play a factor in his decision, adding that he might decide to use Eveland -- on two days of rest after throwing more than 90 pitches for the River Cats on Friday -- in relief.
"This would normally be his [bullpen] day," Geren offered.
Asked if Gonzalez not appearing in Monday's game would tip the scales in his favor for Tuesday, Geren said no. The skipper didn't want to concede that Fenway Park is tougher on lefty pitchers, either, noting that the Red Sox's splits against righties and lefties are "pretty even."
Eveland has an 18.90 ERA in two career starts against the Red Sox and gave up nine runs in two innings at Fenway last season.
Mychael Urban is a national writer for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.