Snow has fallen intermittently in the northern city throughout the day and the referee, having initially delaying the kick-off by one hour, finally decided the pitch at the Atleti Azzurri d'Italia stadium was unplayable shortly before 1900 local time.
A statement from Atalanta read: "For safety reasons, the game between Atalanta and Genoa has been postponed."
This is the fourth fixture this week to be called off because of the ongoing bad weather in northern Italy, where night-time temperatures are expected dip below minus 10 degrees centigrade in the coming days.
Earlier on Wednesday, matches at Bologna and Siena scheduled for the evening also fell foul of the elements.
Bologna were due to host Fiorentina at the Renato Dall' Ara stadium while Siena were set to face Catania at the Stadio Artemio Franchi.
Tuesday's match between Parma and league leaders Juventus was also called off due to heavy snow.
New dates for the fixtures have yet to be confirmed.
Wednesday night's remaining fixtures at Cagliari, Inter Milan, Lazio, Napoli and Udinese are all set to go ahead, along with Thursday's encounter between Novara and Chievo.
The cold snap could also affect this weekend's Serie A programme.
The expected deterioration in the conditions has already prompted AC Milan vice-president Adriano Galliani to write to the president of the Lega Serie A, Maurizio Beretta, to request that Sunday's match with Napoli at the San Siro be postponed.
Temperatures could reach minus 15 degrees centigrade in Milan overnight on Saturday.
"All the weather forecasts for the next few days, and in particular for the weekend, prove weather conditions to be prohibitive, as we have not seen for 27 years in Milan," Galliani wrote to Beretta in a letter reproduced in part by La Gazzetta Dello Sport.
Galliani also claimed that Napoli president Aurelio De Laurentiis was in agreement with his request, saying: "It is a stance shared. You can not play in certain weather conditions."
Parma president Tommaso Ghirardi has also cast doubt on his side's weekend fixture at Chievo, claiming that his team "will not take the field" if he has concerns about the state of the pitch at the Stadio Marc'Antonio Bentegodi.