The 27-year-old, who has been in excellent form, was forced off during last weekend’s 1-0 win over Sheffield United and boss Slaven Bilic has confirmed he will miss between four to six weeks.
Bilic said: “I knew straight away. When I saw Conor needed to be subbed, he is not that kind of guy.
“I hoped it was nothing major and thank god it isn’t but he is going to be out between four to six weeks.
“Knowing he is a good healer and a great character, he will be desperate to come back.
“It is a blow of course, especially considering how well he was doing. But we were concerned it would be a lot worse.”
The timing is unfortunate for Albion, who must now hope Kieran Gibbs is fit enough to replace Townsend for Sunday’s visit of Crystal Palace.
Gibbs was among several members of the Baggies squad to test positive for coronavirus during the recent international break and only returned to training this week.
Club captain Jake Livermore, another to contract the virus will also be assessed ahead of Sunday after sitting out the last two games.
“We have no new cases,” said Bilic. “Jake is back in training. We will see how he is tomorrow.
“We had a rough period during the international break when we had I think more than 15 cases of players and staff. Thank god we are through it.
“Kieran didn’t train for 20 days because of the injury and corona. We will see tomorrow. He has been training for five days now and we will see.”