The game will be made up on Monday afternoon, Aug. 19.
The Twins announced the decision about four hours before the scheduled game. On Sunday morning, light snow was falling, and the forecast called for rain and a high of 38 degrees.
"We certainly knew the day's forecast was not promising," Twins president Dave St. Peter said. "The best decision for the Twins and the Mets, and ultimately for our fans, was to postpone today's game."
New York won the first two games of the series at Target Field, with temperatures in the low 30s.
It's the sixth time the Twins postponed a game since moving from the climate-controlled confines of the Metrodome to Target Field in 2010.
The Mets are scheduled to stop in Minneapolis on Aug. 19 after finishing a weekend series in San Diego before heading back to New York. The Twins are at home the day before and play at Detroit the day after.
Dillon Gee (0-2) was scheduled to start for New York and Kevin Correia (0-1) for the Twins. The projected rotation has Gee pitching on Monday at Colorado, where the Mets aren't exactly expecting warmer conditions - forecasts called for snow in the Denver area and highs in the low 40s.
Correia's start was bumped back to Monday against the Los Angeles Angels.
"I'm sure those guys will take the day off and regroup and hopefully get a precipitation-free day tomorrow," St. Peter said.
The Twins also suspended a game against the New York Yankees after five innings because of rain during the ballpark's inaugural year.
"The first three years have been great, to be honest, much better than many people had predicted," St. Peter said of the weather for outdoor games.