The 26-year-old from Bready is expected to be sidelined for between six and eight weeks.
"Craig will undergo more investigative tests on the injury to decide whether he will require surgery," said a Cricket Ireland spokesperson.
Ireland face Sri Lanka at Malahide on 16 and 18 June.
A Cricket Ireland statement read: "He will miss the games against Sri Lanka, but we would be hopeful he will play a full part in the five-match one-day series against Afghanistan in July."
Young, who has played nine ODIs and 10 Twenty20s, signed for Hampshire on a short-term loan deal in April.
Ireland seamer Craig Young has been ruled out of the two one-day internationals against Sri Lanka in June with an elbow injury.