Burke, a summer capture from Germany’s RB Leipzig, came off after just 18 minutes of an Under-23s match on Monday with a tight hamstring.
The 20-year-old had a scan on Tuesday to asses the injury and the tests have cleared him of any major problems.
Burke, who made his second Premier League appearance of the season as a substitute in Albion’s 3-1 loss at Brighton at the weekend, could yet be involved when the Baggies entertain the Hammers.
However, the Scotland international will require a late fitness test ahead of the game and head coach Tony Pulis may opt to rest him.
Michy Batshuayi's cheeky backheel was enough to give Borussia Dortmund a 1-0 win over Hannover 96 at Signal Iduna Park on Sunday, lifting them within a point of second-placed Schalke.
Eintracht Frankfurt boss Niko Kovac felt his side could have scored more goals following their 3-0 defeat of Mainz on Saturday.
West Brom manager Alan Pardew refused to fault his players' efforts after a heartbreaking 2-1 loss to Bournemouth that dashed their already slim survival odds.