Warriors, confirmed the news on X, adding: "We're all behind you, Z - we know you'll come back even stronger."
The 29-year-old last featured for Glasgow in early April and was absent as they lost Saturday's URC play-off semi-final to Leinster in Dublin.
Capped more than 70 times by Scotland, the tighthead toured South Africa with the Lions in 2021 and featured against Sigma Lions.
Fagerson is replaced by Ireland's Finlay Bealham. Australian-born Bealham, who qualifies for Ireland through his grandmother, moved north in 2010 and made his international debut in 2016.