Yarmolenko, was born in Russia to Ukrainian parents, who then moved back to their homeland when he was a child, was given compassionate leave by the Hammers this week.
It follows Russia's invasion of Ukraine, with the shocking and distressing scenes sparking condemnation across the world.
David Moyes said Yarmolenko was 'not in a good position at the moment' and confirmed he had been given a few days off.
His West Ham teammates showed their solidarity before their game with Wolves.
Declan Rice held up Yarmolenko's Hammers shirt as the teams walked out at the London Stadium.
A message was also displayed on the big screen at the stadium that read: "Sending love and prayers to Andriy Yarmolenko and the people of Ukraine."
The Wolves players also wore 'No To War' t-shirts while warming up before the game.
While Yarmolenko was absent from the match, Man City's Oleksandr Zinchenko and Everton's Vitaliy Mykolenko were involved in the match at Goodison Park.
The pair were reduced to tears as players, staff, and fans showed support for their country of Ukraine before the Premier League clash.
The Goodison crowd roared into applause when the pair hugged during the warm-up, and then showed even more support with Ukrainian flags, shirts and messages for the players, as well as playing the song, 'He ain't heavy, he's my brother'.