Blum's death at the age of 69 was confirmed by his representative on Thursday.
Posting about the sad news on Instagram, the Queen of Pop urged fans to stay home to slow the spread of the illness and to take the advice seriously.
Sharing photos of them together in the 1985 film on Instagram, she wrote: “I Want to Acknowledge the Passing of a remarkable Human, fellow actor and friend Mark Blum, who succumbed to Coronavirus.
“This is really tragic and my heart goes out to him, his family and his loved ones," Madonna continued.
“I remember him as funny warm, loving .and professional when we made Desperately Seeking Susan in 1985!!
“Another reminder that this virus is no joke, nothing to be casual about or pretend wont affect us in some way. We need to stay grateful -be hopeful- help each other-and follow the quarantine rules.”
The off-Broadway theatre company Playwrights Horizons announced the news of Blum’s death.
His recent Broadway credits included The Assembled Parties, Twelve Angry Men, Gore Vidal’s The Best Man – twice – and Neil Simon’s Lost In Yonkers.
Blum also starred in Crocodile Dundee as the newspaper editor and appeared in the Netflix stalker drama You.
Additional reporting by Press Association