Philander, who signed for Sussex in December, will now be unavailable for the Sharks in their One-Day Cup games.
The 31-year-old South Africa international is expected back for four County Championship games before his contract ends in the middle of June.
He scored 21 runs and failed to take a wicket as Sussex lost their season opener to Kent by 226 runs.
Meanwhile, Sussex have confirmed that they have brought in former Leicestershire opening batsman Angus Robson on a season-long trial.
The 25-year-old, who left the Foxes by mutual consent on 11 April, will be able to play for Sussex's second team with a view to earning a contract for next season.
Sussex all-rounder Vernon Philander will miss two to three weeks after suffering a groin injury against Kent.