Bung Moktar Radin drew a flurry of criticism with his tweet: "Well done . Bravo . Long live Hitler ." after Germany thrashed Brazil 7-1 on Tuesday.
Najib called the remarks "unacceptable and wrong."
"He does not speak for Malaysia, or for ordinary Malaysians, who understand Europe's tragic past, and respect its modern unity," Najib said in a statement.
An opposition party called for the lawmaker to quit, and German Ambassador Holger Michael slammed the "unacceptable allusion to the fascist regime of Adolf Hitler."
Bung Mokhtar, who earlier said he was commending the German team for "fighting like" the Nazi leader, issued an apology shortly after Najib's rebuke.
"When Germany whacked Brazil, I unintentionally said something that hurt" the feelings of the people in Germany, he tweeted, adding: "My sincerest apology. Long live Bung."
Some on social media said his apology was insincere.