Babos, 21, has made six appearances for the Rams Under 23s side this season.
He has represented Wales at Under 21 level.
A club statement said: "Neil Reynolds has worked hard to bring in additional talent as the team has a number of injuries and challenges around player availability. Signing Alex is a real coup, particularly as he’s coming from a Championship club.
"We’d like to place on record our gratitude to Derby County for agreeing to this loan."
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