In a statement the Welsh Rugby Union said: “Further assessments (of Lane’s injury) will be concluded early next week to establish an accurate prognosis.”
Lane, 21, has two international caps, scoring a try on his debut against Ireland during August 2019.
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WATCH: Welsh legend Jamie Roberts fronts up to the media at Newlands
Liam Williams is still not fit, having been out of action since suffering an ankle injury in the World Cup in Japan.
The teenager went off injured during his side’s Champions Cup defeat against Toulouse on Sunday.
However, Pivac revealed Rees-Zammit should return when Wales travel to Dublin for the fixture on February 8.
Warren Gatland ended his 12-year tenure following Wales’ World Cup semi-final defeat against South Africa, with Pivac taking over.
WATCH: Head coach Eddie Jones and captain Owen Farrell hold a press conference in London ahead of the start of the Six Nations tournament.
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