Central defender and stand-in captain O'Shea has not missed a single minute of Championship action this season – one of only two players in the league to do so – but will not feature again this term due to a knee injury suffered with his nation in this week's clash with France.
Midfielder Molumby has enjoyed a fine breakthrough campaign with the Baggies but will not play a big part in the remaining nine games of the season due to a groin problem.
Head coach Carlos Corberan revealed a four-week recover period for Molumby, which covers the month of April in which Albion play eight of their remaining nine games.
For O'Shea it is a second serious setback sustained with his country. The academy graduate broke his ankle on Ireland duty in September 2021 after an impressive start to the season under Valerien Ismael and did not return until February 2022.
The double blow arrives at a decisive period for Corberan and his side, who return to action for the first time in 17 days at home to sixth-placed Millwall tomorrow in a clash that had been dubbed make-or-break for their top-six ambitions.
The Hawthorns head coach, who already has wing duo Matt Phillips and Grady Diangana out for the season, was in typically bullish mood and challenged other members of his squad to grasp on opportunity in place of O'Shea and Molumby.
Corberan said: "It's always a challenging period. We know that these next nine games are going to come basically in the next month.
"We know we play a lot of games, but being honest I still have headaches to select the first XI for tomorrow. I have doubts in three positions about who is going to play!
"It means that the players in my mind tomorrow for the bench could be in the first XI. This is completely true. At the same time, we have Bartley – who is an important player and the fact we have him is positive.
"Of course, it's a pity because I want to have all of my players all the time. It's true that when you create a squad with many possibilities in each position, it's uncomfortable for the coach to put someone out of the squad when everyone is fit.
"At the same time, you have the possibility to put someone in when somebody is missing. You know the team will compete because I believe a lot in the players that I have."
There was better news that defender Kyle Bartley – who has not played for more than six months – had recovered to train fully during the international break and comes into contention as O'Shea's replacement.
Semi Ajayi featured for Nigeria in the break and reported back in good condition, as did striker Daryl Dike, who played twice for the United States.
Attacker Karlan Grant has not featured since the defeat at Watford over a month ago but returned to training on Friday.
Goalkeeper Alex Palmer, though, is not yet ready to challenge for the No.1 shirt with Josh Griffiths. Palmer is taking part in sections of training but is still experiencing pain when kicking, so England under-21 international Griffiths and David Button will once more be included in Albion's 18.
Corberan said Taylor Gardner-Hickman, Nathanael Chalobah and Adam Reach are options to replace Molumby in midfield against the Lions tomorrow, while Ajayi – who played 90 minutes at Cardiff before the break – and the returning Bartley are options to replace O'Shea.
"In a dressing room, with the level of support they have between them, nobody is going to be happy about this," Corberan said of the double setback.
"But at the same time, I know that Ajayi, for example, was desperate to play and have this opportunity. Bartley has been out for a long time and he is desperate to play too, they want to help the team.
"Gardner, Chalobah – Molumby has been playing, but we have in those and even Reach, I see him to play as a number eight without any doubt, they have now (the chance), which unfortunately arrived because of an injury to another player which nobody is happy about, never, they respect a lot and have a very strong relationship.
"But at the same time now they have an opportunity for them, they need to prove (it), I can play tomorrow with Chalobah, Gardner, Reach, and I know I can put a strong team."