FA Cup holders Manchester City face a trip to Newcastle United in the quarter-finals.
Pep Guardiola's men were unconvincing in their fifth-round clash with Championship side Sheffield Wednesday, Sergio Aguero scoring the only goal in a 1-0 win.
City's reward is a trip to St James' Park, where they were held to a 2-2 Premier League draw in November.
Chelsea, who knocked out runaway Premier League leaders Liverpool on Tuesday, will visit fellow Champions League chasers Leicester City.
Arsenal's quest to extend their competition record to 14 titles next takes them to Bramall Lane, the Gunners having suffered a 1-0 defeat there in October when Unai Emery was still at the helm.
Derby County, the sole remaining non-Premier League side in the competition, will travel to Norwich City should they stun Manchester United on Thursday.
Wednesday's clash between Tottenham and Norwich was locked at 1-1 in extra time, but Tim Krul denied Gedson Fernandes in a penalty shoot-out to send the Canaries through.
The quarter-final matches will be played on the weekend of March 20-22.
Draw in full:
Sheffield United v Arsenal
Newcastle United v Manchester City
Norwich City v Derby County/Manchester United
Leicester City v Chelsea