"We condemn this heinous attack and see that the response to this crime is in the hands of those concerned in Iran," Sheikh Naim Qassem said in an interview with Al Manar television.
He said Fakhrizadeh was killed by "those sponsored by America and Israel" and said the assassination was part of a war on Iran and the region. Iran pointed the finger at Israel after Fakhrizadeh was killed in an ambush near the Iranian capital Tehran on Friday. Israel declined to comment.
Earlier this month, Hezbollah leader Sayyed Hassan Nasrallah said Iran's allies in the region should be in a state of high readiness in case of any "American or Israeli folly" during the remainder of US President Donald Trump's term.
Asked whether Israel could attack Lebanon during that time, Qassem said he did not believe so but that if it did Hezbollah was "fully prepared" for a confrontation.
Israel and Hezbollah last fought a war in 2006.
Qassem said it was unlikely there would be a direct strike on Iran as it would "ignite the whole region.""We cannot rule out the possibility of a limited attack and the Iranians are ready for this and more, but I don't see an all-out war on the horizon," he said.