Nowell fractured his cheekbone in Saturday's victory against Newcastle Falcons and there is the possibility the wing will require surgery, meaning he could potentially be out for around eight weeks.
The 24-year-old has established himself as a key member for England since making his international debut in 2014, whilst he was also part of the British and Irish Lions squad for the 2017 tour of New Zealand.
Eddie Jones' side face Argentina, Australia and Samoa in successive weeks from November 11 and Nowell, who will definitely miss Exeter's ties against Glasgow and Montpellier in the European Champions Cup and Sale in the league, could miss all three autumn Tests.
"He's got a couple of fractures in the top of his check and eye socket," Baxter told BBC Sport. "It's still a little early to write him off for the whole of the autumn internationals, that's something we're going to have to assess in the next week or so.
"It's always a blow when you lose good players, that's why you put a squad of people together, but we're big believers here that if one person picks up an injury it's an opportunity for someone else."