Hogg was withdrawn early on in a 22-13 defeat to Ireland at Murrayfield on Saturday after a collision with Peter O'Mahony.
The British and Irish Lions full-back will visit a specialist on Wednesday to discover the extent of the damage.
Townsend is optimistic the Glasgow Warriors star is not facing a lengthy absence.
"He's about to see a specialist later today, so we'll know more about his chances of playing over the next few weeks after that." Townsend said.
"I'm very hopeful that he'll get good news and that he'll be available to play some part in the Six Nations."
Townsend believes Scotland have ample quality in the backline if Hogg is ruled out.
"Blair [Kinghorn] obviously had a great game against Italy," he said. "He backed that up with his first touch as he got through the Ireland defence on Saturday and was heavily involved in the second half.
"We've got good strength and depth in the back three. Tommy Seymour and Sean Maitland have both played at full-back and are both very experienced players.
"I believe Byron McGuigan is back for his club this week, so if Stuart is missing - and I really hope that's not the case - then we do have other players who are in really good form."