The Red Devils winger will remain with the Tigers until 2 January, while United team-mates Michael Keane and Jesse Lingard have also extended their loan deals with Leicester City.
The 20-year-old Republic of Ireland international joined the Tigers on an initial one-month deal at the start of November and has made six appearances for Steve Bruce's side as they look to secure promotion back to the Premier League after a three-year absence. His final match will now be the trip to Blackpool on January 1.
Brady, who scored one and set up a further two on his international debut against Oman back in September, spent the 2011-12 season on loan at the KC stadium, making 41 appearances for the Tigers, scoring three times. Hull are currently fifth in the table, five points off the top two spots.
Meanwhile fellow Red Devils starlets, Michael Keane and Jesse Lingard have also extended their respective loan deals at Leicester City for a further month, meaning they too will stay out on loan until January 2.
Attacking midfielder Lingard, 19, has made four appearances while at the King Power Stadium.
Centre-half Keane, also 19, returned to his parent club after sustaining a hamstring injury during his Foxes debut at Bolton Wanderers but is close to full fitness.
Both will now be available for home games against Barnsley, Cardiff City and Huddersfield Town - along with away trips to Millwall, Hull City and Burnley.