Referee Ian Davies called off the contest following a prolonged spell of lightning and hailstones.
Zebre had been leading 22-10 against the reigning Guinness PRO12 champions at half-time but because the game was abandoned after only 40 minutes, the fixture is null and void and will be replayed from the start.
Zebre coach Guidi said: "The safety of the players must always come first. Of course we are disappointed it was stopped when we were in such a good position, but there was nothing which could be done."
Tommaso Boni, Maxime Mbanda and Jacopo Sarto had gone over for Zebre in the opening period, with full-back Tiernan O'Halloran scoring for Connacht.
And their head coach Pat Lam also believes the game should have been called off.
He said: "It was the correct decision, safety is the first priority. Nobody expected the lightning and the rain and the hail, and then once it went past 20 minutes, it is out of control of both teams."