The game in the capital was originally scheduled for 14 December but was postponed due to a COVID-19 outbreak in the Reds' squad, which led to Carrington being closed for first-team operations.
The Premier League has confirmed it will now be played on Wednesday 19 January, with a 20:00 GMT kick-off.
It is our first competitive fixture with the Bees since 1975, and the last United away game against the south-west Londoners was way back in 1947 – a goalless draw at Griffin Park.
However, the two sides played a pre-season friendly at Old Trafford last summer, which ended 2-2.