The hard-left official was rejected in the short-listing process after a selection panel interview. It is understood he had been backed by just three constituency Labour parties (CLPs).
Nicky Brennan, who was appointed by Mr Foster as the region's victims' commissioner, has made the final two and will face off against former corporate accountant Richard Parker.
Mr Parker, who has positioned himself as the centre-left candidate and led the way with 17 constituency nominations, said his campaign had received "overwhelming" support.
He said: "With online ballots opening soon, I relish the opportunity to engage with even more members from across our movement. I believe I am the candidate that reflects our shared Labour values, and can unleash our region’s full potential. I know I am the candidate who Andy Street fears the most.
"I won’t rest until we have an integrated, affordable and publicly controlled transport system in the West Midlands. I will lead an all-out assault on low pay to help those suffering from the cost of living crisis. And we will go green quicker to save our planet and create well paid jobs in the region."
Nicky Brennan is understood to have received eight nominations, with CLPs allowed to nominate a woman candidate as well as a first choice in order to ensure a "fair gender balance".
She said: "I'm the candidate that's going to give Andy Street his P45! I'm on the shortlist, now let's win this for Labour so we can win for the West Midlands."
The final candidate, who will attempt to become the region's first Labour mayor, will be selected following a vote of members.
Local hustings are due to take place in the coming weeks, with the result set to be announced on April 14.
Conservative Mr Street won the region's first two mayoral elections in 2017 and 2021.