The 126 plaintiffs claim their electric vehicles don't accelerate from 0 to 100 kph in 3.3 seconds, as marketed.
"At the core of the matter is that there are consumers seeking compensation because the cars have less horsepower than promised," one of the lawyers for the owners, Kaspar Thommessen, told AFP without specifying the amount of damages sought.
They are suing Tesla for breach of consumer law.
The dispute concerns the Tesla S P85D, a sedan featuring one of the fastest accelerations in the world, listed at 700 horsepower by the carmaker. But according to the dissatisfied owners, the real horsepower is only around 469, making accelerations a little less spectacular than expected.
"Some may think that this is just whinging," Tesla owner Frode Fleten Jacobsen told business daily Dagens Naeringsliv.
"But many people pushed their financial limits in order to own a car with 700 horsepower, and when you notice that you didn't get what you paid for you feel cheated," he said.
He said he dished out 873,900 kroner (about €94,000, $105,350) for his car.
Tesla Norway meanwhile said its tests and those conducted by third parties showed that the car consistently performed as marketed, or better.
"With respect to acceleration, Tesla described the S P85D as having a 0-100 kph time of 3.3 seconds, and Motor Trend and others actually achieved a time of 3.1 seconds," a Tesla spokesman wrote in an email to AFP.
The case will go before an Oslo court in mid-December.
Norway, where electric cars are exempt from taxes, is one of Tesla's biggest markets. The company has sold more than 1,600 cars so far this year.
In August, zero emission cars -- all brands combined -- accounted for more than 15 percent of new car registrations, a market share which is unparallelled in the world but which is facing stiff competition from hybrid cars.