Quins were leading Tigers 20-6 when debris was blown onto the pitch in gale-force winds forcing referee Gwyn Morris to call off the game with 10 minutes remaining.
The organisers of the LV= Cup issued a statement, which said: “Following the abandonment of Harlequins v Leicester Tigers in today's Round 3 LV= Cup match, the LV= Cup Organising committee will review the circumstances under which the match was abandoned once it has received all the relevant information.
“A further update will be provided in due course.”
The home side Harlequins issued a statement through the official club website, which said: “Due to the extreme weather conditions, Harlequins had to call off the third round LV= Cup match against Leicester Tigers after 70 minutes and eight seconds.
“As a result of very strong winds, parts of the stadium were blown onto the field of play and so the game was abandoned to ensure the safety of players and supporters.
“The Club would like to thank stewards and staff for their swift reactions and the supporters of both teams for their understanding in the circumstances.
“The Tournament Organising Committee will decide whether the score at the time of abandonment will stand or if the fixture needs to be replayed. Harlequins will inform our supporters as soon as a decision is made.”