The Portuguese player, 19, joined the Tykes from Liverpool last summer but has managed just one substitute appearance for the Championship club this season.
He does, however, have experience of League Two football having spent the back end of last term on loan at Northampton.
Interim manager Wayne Burnett told the Daggers' official website: "I'm absolutely delighted to have obtained the player and would like to thank Barnsley manager David Flitcroft for making this deal possible.
"The player was signed from Liverpool with a lot of promise. Unfortunately, he has slightly lost his way, but hopefully we can get him back to his best."
Silva is available to make his Dagenham debut in Good Friday's trip to Barnet.