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."
"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.
