The lawsuit, filed on behalf of resident Terry Gillman, charges Sprint with issuing unsolicited commercial e-mail without permission of the recipients and without an ongoing business relationship.
Utah's "Unsolicited Commercial E-mail Act", which bans businesses from sending unsolicited e-mail, known as spam, came into effect on 6 May.
The law says that commercial e-mail may be sent legally as an advertisement if it includes the characters "ADV:" at the beginning of the subject line in the e-mail. With such labelling in the subject line, a recipient can choose not to view the message on its face or can set up e-mail filtering software to automatically delete such messages.
Despite the new law, according to the plaintiff, Sprint sent out the messages, which included offers for a Sprint telephone service. The message did not include "ADV:" in the subject line, according to the plaintiff.
Sprint spokesman Travis Sowders said the company would not comment on pending litigation. However, in a written legal response to the plaintiff, Sprint attorneys called Utah's law "void on its face" because it violates the US Constitution, which guarantees free speech, due process and free commerce.
Sprint's statement denies that unauthorised e-mails were sent and said that any unsolicited e-mails that were allegedly received were "transmitted accidentally and/or after implementation of reasonable measures" to prevent them.
Under Utah's new law, violations are punishable by fines of $10 (£6.40) per illegal commercial e-mail sent, up to a maximum of $25,000 (£16,000) per day that the violations occur. The fines or actual damages are awarded to the plaintiffs, under the law.
Denver Snuffer, an attorney representing Gillman, said the suit was filed because unsolicited e-mails are an unfair burden on his client's time.
Gillman accesses e-mail at work, in libraries and in coffee shops, Snuffer said. The problem is that such access is often with strict time limits, which is then wasted going through unsolicited commercial e-mails.
"This is supposed to be a speedy, easy way for people to communicate," Snuffer said. "To be able to use it, we need to do something to [get] the junk out, and the interference with commerce that spam constitutes."
Jason Catlett, president of Junkbusters, a privacy group, said laws such as Utah's are fairly common, but they fall short of actually banning unauthorised commercial spam from being sent out.
"State laws should prohibit spamming period," Catlett said, "not merely require labeling. That's an incidental public policy move."
The lawsuit, if ultimately successful, bears watching, he said. "If Sprint was really spamming, then they deserve to be caught." he said.