Earlier Monday, a league source had told ESPN NFL Insider Adam Schefter that a fine was expected for Smith, although a suspension was unlikely.
Smith was ejected in the second quarter after pushing back judge Steve Freeman aside during a confrontation with several Titans players in Minnesota's 30-7 victory.
It was the first time a player has been ejected from a game this season, and just so happened to come with commissioner Roger Goodell watching from a Metrodome suite.
NFL spokesman Greg Aiello said Smith's disqualification from the majority of the game was a "significant penalty."
"Right after it happened, I realized I put my hands on the official," Smith said. "You just can't do it, period. So, I apologize to him. I apologize to my coaches, to my teammates, to the fans. It's just unacceptable."
Also Monday, Frazier said the Vikings are trying to determine why wide receiver Jerome Simpson woke up with numbness and weakness in his lower left leg before Sunday's game against Tennessee.
Coach Leslie Frazier said Simpson was undergoing MRI tests on Monday. Simpson played in parts of Minnesota's 30-7 win, but he didn't catch any passes. He had trouble pushing off because of the injury, which Frazier said could also be connected to his back.
Frazier said Simpson was "alarmed" by his condition but that the Vikings don't believe he's facing a long-term absence.
Running back Adrian Peterson suffered a mild sprain of his left ankle that he played through. Frazier said the Vikings don't see "anything that will keep him from playing" on Sunday at Washington.
Smith has been one of the biggest keys to the surprising resurgence of the Vikings' defense, and he's quickly gained a reputation as an aggressive, hard-nosed player. He was fined for an illegal hit in the preseason and found himself in the middle of a trash-talking session with a handful of Titans after Antoine Winfield intercepted a pass from Titans quarterback Matt Hasselbeck.
Freeman stepped in to try to steer Smith away from the area and was guiding Smith back when the safety pushed him to the side to get back in the mix.
"He grabbed the official," referee Jeff Triplette said. "The official was trying to separate him and he pushed the official to the side. That's an automatic ejection."
Smith said Sunday when asked about any possible NFL punishment that he would "take whatever they give me."
"The officials already have a hard job and I should never have been there. I just want to play next week and just help the Vikings win," he said.
Information from The Associated Press was used in this report.