Jim Mallinder’s men host Leicester Tigers in the Aviva Premiership on Saturday, March 29 in a game that will be shown live on BT Sport with a 3.15pm kick-off.
They must then travel north to the AJ Bell Stadium for the European tie against the Sharks on Thursday, April 3.
That game will kick-off at 8pm and will be shown live on Sky Sports.
Saints will at least have plenty of time to recover ahead of a crunch league game at Saracens on Sunday, April 13.
The game at Allianz Park will be broadcast live on BT Sport with a 2pm kick-off.