The Albion midfielder suffered damage in an awkward tangle with Evanilson early at Bournemouth and is facing a lay-off.
He told followers via social media: “Not the start to the game I anticipated.
“I’ll be back out there soon, thanks for your support.”
Hinshelwood has suffered injury setbacks in the last two seasons and made 22 Prem starts last term.
Diego Gomez appears to be back in training after missing the trip to Dorset.
Gomez started the most recent home fixture, against Manchester City, and played down a knock suffered early in that game.
He then played twice for Paraguay but was left out of the matchday squad to face Bournemouth having been involved in the most demanding international window of Albion players when taking into account minutes played and miles travelled.
Fabian Hurzeler will have the option of starting with James Milner and Yasin Ayari against Tottenham on Saturday – the combination he used for most of the game at the Vitality Stadium.
He will also hope for a return to form for Carlos Baleba.