The game at Pittodrie on Sunday, 5 March kicks off at 15:00 GMT with TV coverage also streamed on the BBC Sport website.
The other last-eight ties are Rangers v Hamilton Academical, Hearts or Hibernian v Ayr United (both 4 March) and Celtic v St Mirren (5 March).
All four quarter-final ties will be covered on BBC Radio Scotland.
There will also be highlights on Sportscene and the BBC Sport website across the weekend.
Hibs host Hearts in their fifth-round replay on 22 February.
On Tuesday, Accies beat Dunfermline Athletic on penalties to secure a visit to Ibrox while Ayr beat Clyde after extra time.
Saturday, 4 March
Rangers v Hamilton Academical (12:30)
Hearts or Hibernian v Ayr United (15:00)
Sunday, 5 March
Celtic v St Mirren (12:30)
Aberdeen v Partick Thistle (15:00)
BBC Scotland will show live coverage of the Scottish Cup quarter-final between Aberdeen and Partick Thistle.