Suarez, 27, suffered the injury recently in a swimming pool, according to the Reds. He is expected to be ready to play "near the beginning of the regular season."
He posted career highs in home runs (49) and OPS (.930) last season.
The Reds are making a major push to win the National League Central, having committed up to $164 million in free agents this offseason.
Cincinnati most recently added Nicholas Castellanos ($64 million) to a free-agent crop that includes Mike Moustakas ($64 million), outfielder Shogo Akiyama from Japan ($21 million) and pitcher Wade Miley ($15 million).