The 23-year-old American pop star was due to perform two shows at the O2 Arena on Thursday May 25 and Friday May 26.
There has yet to be any official word on whether the concerts will still go ahead.
A spokesman for the O2 Arena said: "We are shocked and deeply saddened by the terrible tragedy in Manchester.
"Our thoughts and prayers are with those affected and their families.
"We are in contact with the promoters of Ariana Grande’s tour and will update as soon as we have further information regarding the planned dates at The O2.
"Anyone visiting The O2 should allow extra time for enhanced security checks.
"More details about security at The O2 can be found here."
22 people, including children, died in the Manchester attack and 59 others were injured.
Greater Manchester Police is asking members of the public to avoid the city centre and have stepped up security around the area with armed police patrolling the Trafford Centre shopping mall.
Londoners attending upcoming events across the city, such as The Emirates FA Cup Final on Saturday (May 27) can be assured that there will be extra measures put in place to ensure safety.
A spokesman for the FA said: “Fan safety is of paramount importance and we have robust security measures in place at Wembley Stadium.
"In collaboration with the Metropolitan Police and the local authorities there will be an enhanced security operation for all upcoming events.
"All supporters are encouraged to arrive for events at Wembley Stadium as early as possible for security checks and to avoid any delays in entering the stadium.”
Greater Manchester Police confirmed it has arrested a 23-year-old man in South Manchester in connection with the incident.
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