The striker, who moved to The Hawthorns from Liverpool on loan until the end of the season, pulled up just three minutes into the team's match against Chelsea at Stamford Bridge.
Overall, it was a disappointing evening for the Baggies as they suffered a 3-0 defeat.
When asked about Sturridge's injury woe on BBC Radio 5 live, Pardew said: "He felt his hamstring after a 60 metre full sprint in the first moments of the game. He's had to come off. We'll have to nurse him. He won't play next week but hopefully the week after."
On the game itself, Pardew said: "When you go to a top six team who are wounded a little bit, we had a great chance to hurt them. We missed a great chance and five minutes later we were 1-0 down. Our poise in the game was good and we still created chances.
"We just couldn't hurt them. Once they got the second goal you could see the relief in the team and the crowd. There have been so many drawn games we should have won."*
The club sit at the bottom of the Premier League table due to just three wins in 27 matches.