The England international lead the line for the Hammers in Saturday's 2-1 victory at Wolverhampton Wanderers in the Premier League.
However, Bowen was forced off just nine minutes in the second-half following an innocuous collision with Wolves midfielder Mario Lemina.
Bowen attempted to play on, but it quickly became clear that the attacker was unable to continue and he eventually limped off down the tunnel to receive treatment.
West Ham were trailing at half time after Pablo Sarabia scored the opener for Wolves from the penalty spot, but after Bowen's withdrawal, the Hammers turned the game on its head in the second half thanks to strikes from Lucas Paqueta and James Ward-Prowse.
David Moyes delivers Jarrod Bowen injury update
Hammers boss David Moyes has confirmed that Bowen sustained a hip injury against Wolves and is hopeful that the attacker's problem is not as serious as initially feared.
"We've got to hope he's OK. We need all our top players," Moyes told reporters after the match as quoted by the Evening Standard.
"He's had a knee into his hip or back. It's not a twist. He said he's got kneed and he's really stiff.
"I've had one or two of those myself and they don't go away too quick. I'm hoping it won't be too bad."
West Ham remain seventh in the Premier League table despite their win over Wolves, but they have moved level on points with sixth-placed Manchester United, who play host to leaders Liverpool on Sunday.
Can West Ham cope without Bowen?
Bowen has been standout performer for West Ham this season and is the club's top scorer with 19 goals in 39 appearances across all competitions.
The 27-year-old has chipped in with one goal and three assists across six Europa League matches this term, while he contributed with five goals and two assists in the Hammers' triumphant Europa Conference League campaign last season, including three goals in the knockout rounds - one being the match-winner against Fiorentina in the final.
Bowen's importance in attack for West Ham is unquestionable and his potential absence for a Europa League quarter-final first-leg tie in Germany against high-flying Bundesliga leaders Leverkusen will be a concern for Moyes and co.
Should Bowen failed to recover in time, Michail Antonio is the most likely candidate to lead the line for West Ham, although he has only scored four goals in 25 games so far this season.
Danny Ings is another option to lead the line, but he has been a peripheral figure under Moyes this term and has been reduced to just six starts in all tournaments, scoring only once.
Versatile attacker Mohammed Kudus is West Ham's second-top scorer this season with 12 goals and he could be deployed as a centre-forward, but he has predominantly played on the right side of attack where the Hammers are limited for options.