The powerful loosehead was forced off in his team’s 23-21 Guinness PRO14 victory over Leinster on Saturday night with what Pivac initially described as a shoulder or pectoral injury.
Pivac also saw Johnny McNicholl, Josh Macleod and Jake Ball join Evans in leaving the field against Leinster, but the news on all four men is upbeat.
“It’s good news actually. Rob is a bit sore and Josh is the same, but no surgeries are required so that’s very pleasing. We’ll reassess them again next week,” Pivac said.
“We’ll have to wait another week and we’ll have a better idea on timelines then. Rob’s probably the best scenario and hopefully we will have him in back in two to three weeks.
“Johnny will be training fully on Tuesday and Jake is training too.”
Scarlets got their season up and running against Leinster, but will still be without Wales and British & Irish Lions centre Jonathan Davies for the next few weeks.
The midfield ace is currently nursing a hamstring problem.
Scarlets are at home to unbeaten Italian side Benetton on Saturday.
“We’re not rushing Jon. We want to get him 100 per cent right. There’s a lot of big rugby coming up and we’re doing OK in the centre position at the moment,” Pivac said.
“The way things have gone for us so far this season we’re quite happy with how those results have turned out.
“Wyn Jones trained fully on Monday and if he comes through scrums on Tuesday he’ll be back in contention for the weekend. Uzair Cassiem is back running and is just around the corner to make a return.
“Dylan Evans has had a bit of a bump to his shoulder, because of what we’ve got coming up we’re rehabbing him.
“With potentially losing two looseheads to the international window we need to be sensible there.”