Murray joins a lengthy injury list at Thomond Park with Mike Sherry (knee ligament) and Tyler Bleyendaal (quad) continuing to follow their rehab programmes this week - both are expected to return to modified training early next week.
Munster medical staff also confirmed that both Peter O'Mahony (ACL) and Duncan Casey (pectoral muscle) underwent successful surgeries last Friday.
But with high-flying Connacht on scintillating form both in the GUINNESS PRO12 and European rugby, Foley knows Munster will be up against it without Murray pulling the strings.
"He got a stamp on the foot in the Treviso game so it was prudent that he didn't run on Tuesday," he said. "Anybody who doesn't train on the Tuesday would be a doubt for the weekend.
"It's about preparation and if you're not properly prepared, you are liable to incur more injuries, so we want fellas to do a full week's work before we play them.
"Connacht were excellent last season, they had a run in Europe as well and we probably got a taste of it in pre-season and they gave us a good trimming (28-12) at Thomond Park.
"From there, they've done really well in the GUINNESS PRO12 and they've won their two European games. They're going really well. With the players they have, they're playing super rugby and they're dangerous."
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