Instead, manager Fredi Gonzalez faces a different problem for the Braves, who were off on Monday: How does he make room for another arm in a rotation enjoying the majors' best opening month in 100 years?
There's no weak link as the starters' 1.57 ERA easily leads the majors.
The rotation was a big question after Tim Hudson and Paul Maholm departed as free agents. The issue reached crisis stage when Kris Medlen and Brandon Beachy needed season-ending Tommy John surgeries in spring training.
Veterans Ervin Santana and Aaron Harang have joined Julio Teheran and Alex Wood as the staff's new leaders on the first-place Braves.
Minor, who was a projected top starter, is expected to come off the disabled list this week.
Rookie David Hale could lose his spot, but it's no easy decision for Gonzalez. Hale is 1-0 with a 2.31 ERA in four starts and is coming off an outstanding win. Hale allowed only two hits over eight innings in a 4-1 win over the Reds on Saturday night, facing the minimum 21 batters over his last seven innings.
A tough call?
''Sure,'' Gonzalez said. ''We're pitching well, we're playing well. You don't want to disrupt that.''
The staff has posted numbers through 24 games unmatched by any modern staff - including the Braves' rotation of the 1990s with 2014 Hall of Fame inductees Greg Maddux and Tom Glavine, plus John Smoltz.
According to STATS, the 1.57 ERA through 24 games matches baseball's best start since the 1914 White Sox opened with a 1.36 mark. The 1915 Phillies starters also had a 1.57 ERA through 24 games.
This year, St. Louis is second in the majors with its 2.24 ERA.
At 17-7, the NL East-leading Braves open a series at Miami on Tuesday night. Wood will face Marlins ace Jose Fernandez in a rematch of a memorable duel on April 22 when the two combined for 25 strikeouts and no walks in Miami's 1-0 win.
Low-scoring games are the rule for the Braves this month. Atlanta completed a three-game sweep of the Reds on Sunday with a 1-0 win in 10 innings, with Teheran matching Johnny Cueto's eight scoreless innings.
The Braves already have played five 1-0 games - including two hard-luck losses by Wood.
''I'd rather have it this way than the other, when you're scoring 14 runs and giving up 13 every night,'' Gonzalez said. ''Our bats will pick up, sooner or later.
''It's fun. Every once in a while, you look at the scoreboard and somebody is beating somebody 8-2 in the ninth and you go, 'I wish I'd get one of those every once in a while,'' he said.
Before this year, the best opening month for a Braves rotation in the modern era was a 2.37 ERA in 1997, according to STATS.
Harang, who leads the majors with his 0.85 ERA, is the biggest surprise. The 35-year-old journeyman was released by Cleveland in spring training and signed with the Braves.
Teheran, seventh at 1.47, said matching scoreless innings with Cueto helps him believe he deserves to be ranked with baseball's best starters.
''Now I feel like one of those guys,'' said Teheran, who was 14-8 with a 3.20 ERA in his 2013 breakout season.
Teheran is only 23.
''I know how good he can be,'' Braves shortstop Andrelton Simmons said. ''He's proving to people that he deserves to be the ace for the team.''
Wood also is 23. Minor and Hale are 26.
Minor was 13-9 with a 3.21 ERA last year. He had urinary tract surgery on Dec. 31, which pushed back his spring schedule. He then developed the shoulder soreness and was shut down in spring training.
Entering this season, Minor had the fourth-best ERA (2.90) since the 2012 All-Star break, so the Braves have to make room for the left-hander.
Hale could be sent to the minors or to the bullpen. An even tougher decision could come soon when Floyd, recovering from Tommy John surgery early in the 2013 season with the White Sox, also is ready.
Gonzalez just shook his head as he avoided the question.
''One at a time, please,'' he said.