Weber hit Zetterberg as time ran out in the third period of the game, the first of a best-of-seven Eastern Conference quarterfinal between the teams. Nashville won the game 3-2.
Game officials issued a 2-minute roughing penalty to Weber. The NHL added the $2,500 fine Thursday.
"We felt this was a reckless and reactionary play on which Weber threw a glancing punch and then shoved Zetterberg's head into the glass," said Brendan Shanahan, NHL senior vice president of player safety and hockey operations.
"We reached out to Detroit and were informed that Zetterberg did not suffer an apparent injury and should be in the lineup for Game 2."
The second game of the series is set for Friday in Nashville.