Bowen is the Hammers' top scorer this season with 19 goals in 40 appearances across all competitions, including a strike in last month's 5-0 second-leg win over Bundesliga outfit Freiburg in the last 16.
The 27-year-old England international was handed a start up front for West Ham in last weekend's 2-1 victory at Wolverhampton Wanderers in the Premier League.
However, Bowen limped off down the tunnel just nine minutes after the interval following a strong collision with Wolves midfielder Mario Lemina.
Moyes and his West Ham squad arrived in Germany on Wednesday evening ahead of their encounter with Bundesliga champions-elect Leverkusen at the BayArena on Thursday, but Bowen has not travelled with his teammates and remains at home in recovery.
Bowen ruled out of Leverkusen clash
Moyes has admitted that Bowen's absence will be felt by West Ham, but the Scotsman is confident that he has other attacking options at his disposal who can step up on Thursday.
"Jarrod's not with us. He's got an injury and he's not available to play tomorrow night. We're not sure about when he might return at the moment," Moyes said at a press conference on Wednesday.
"We think [when he got the knee in his back] he's twisted and he's probably damaged a bit of something, a bit like a fast bowler gets in cricket. It's about the rotation, which is where we think the damage has come from.
"Jarrod will always be a miss because he's a boy who's played a big part in memorable games for us, especially in the UEFA Europa Conference League final last year.
"But, these things happen in football, and we have players ready to come in to try and get the job done for us."
West Ham also without, Phillips, Areola and Alvarez
West Ham will also be without midfielder Kalvin Phillips and goalkeeper Alphonse Areola due to injury, while lynchpin Edson Alvarez is suspended for the first leg.
While Phillips is nursing a hamstring injury picked up in training, Areola remains sidelined with a groin problem sustained in the first half of the Hammers' 4-3 defeat at Newcastle United on March 30.
"Alphonse Areola isn't here with us for this one," said Moyes. "Kalvin Phillips kicked the back of someone's leg in training, and we think he's just tweaked a bit of a lower hamstring, at the back of his knee. I don't think it'll be long-term, but it only happened yesterday so I'm not too sure at the moment.
"Edson's out as well, and we have to find a way to cover that area of the pitch. He does a good job for us in different ways, but we have to play without him."
Lukasz Fabianski is set to continue between the sticks in the absence of Areola, while James Ward-Prowse and Tomas Soucek are both expected to start in centre-midfield, with Moyes potentially switching to a three-man backline to compensate for the lack of central options.
Such a move could therefore see both Vladimir Coufal and Emerson Palmieri operate as wing-backs, while Michail Antonio is expected to deputise up front in the absence of Bowen and be joined in attack by Lucas Paqueta and Mohammed Kudus.