The 21-year-old Northern Ireland international's initial spell was due to end after next Saturday's trip to Oldham, but he has now agreed to stay in west London until May.
Hodson originally joined the Bees in November and has so far made six appearances for Uwe Rosler's side.
Speaking after Saturday's 2-2 draw with Southend in the FA Cup, he said: "I am happy, I am enjoying my time here.
"There are a great bunch of lads, a great manager and great coaching staff.
"The club is in a great position fighting for promotion and it is great to be involved."