The 30-year-old reached the landmark in his 222nd innings, surpassing Indian legend Sachin Tendulkar, who crossed the 11,000-run mark in 276 innings.
When rain stopped play, Kohli, in his 230th ODI, was on 71 off 62 deliveries -- his 92nd 50-plus score since making his debut against Sri Lanka in 2008.
%%%twitter https://twitter.com/hashtag/ViratKohli?src=hash&ref_src=twsrc%5Etfw">#ViratKohliscores his 11,000th ODI run!
He reaches the landmark in 54 fewer innings than anyone else 👀 pic.twitter.com/mebDOLJESs
— Cricket World Cup (@cricketworldcup)
He reached the 11,000 milestone with a boundary off Pakistan paceman Hasan Ali in the 45th over of the Indian innings at Old Trafford.
Kohli, who was also the fastest to 10,000 runs - a milestone he achieved in October last year, is the third Indian to join the elite list.
The star batsman hit six fours in his innings so far, helping India to 305 for four in 46.4 overs when rain interrupted play.