Rothman, a Toronto native who lives in Israel, was "seriously injured" and is now in hospital in "very, very serious" condition, his sister Shelley Rothman-Benhaim said.
"He has undergone several surgeries — one for his head, one for his eye, one for his arm," she said, adding that he is currently in a medically induced coma.
Rothman-Benhaim said her brother is "one of the nicest, sweetest, kindest people in the world."
She said her brother, who lives in Jerusalem, was a "very religious man" who was kind to everybody and was known for gestures like stopping to give hitchhikers a ride.
Rothman is the father of 10 children, she said, and recently became a grandfather for the first time.
Rothman-Benhaim said she was horrified and saddened when she heard of the attack, which occurred in Har Nof, a neighbourhood in West Jerusalem.
Harper calls attack 'barbaric act of terror'
Canadian Prime Minister Stephen Harper condemned the attack, saying on Twitter that it was a "barbaric act of terror."
"Our thoughts & prayers are with the people of Israel," the tweet said.
Four of the dead were rabbis and one was a police officer who died of his wounds hours after the attack. Three of the rabbis were born in the United States and the fourth was born in the U.K., although all held dual Israeli citizenship. Five people were wounded.
U.S. President Barack Obama also condemned the attack, saying "there is and can be no justification for such attacks against innocent civilians."
"At this sensitive moment in Jerusalem, it is all the more important for Israeli and Palestinian leaders and ordinary citizens to work co-operatively together to lower tensions, reject violence, and seek a path forward towards peace."
Israeli Prime Minister Benjamin Netanyahu accused Palestinian President Mahmoud Abbas of inciting violence in the city and said the killings, along with a spate of recent attacks, were part of a "battle over Jerusalem."
"As a nation, we will settle the score with every terrorist and their dispatchers, and we have proved we will do so, but no one may take the law into their own hands, even if spirits are riled and blood is boiling," Netanyahu said in broadcast remarks.
Netanyahu has said that Israel plans on demolishing the homes of the attackers.
2 attackers shot dead
Abbas condemned the attack, which came after weeks of unrest fuelled in part by a dispute over Jerusalem's holiest site, known to Muslims as the Noble Sanctuary, containing the Al-Aqsa Mosque, the third holiest in Islam, and to Jews as the Temple Mount because two Biblical temples once stood there.
Micky Rosenfeld, a spokesman for Israeli police, said the two attackers were shot dead by police during a gun battle outside the synagogue.
The two attackers were identified by police spokeswoman Luba Samri as Ghassan and Oday Abu Jamal, from the Jabal Mukaber neighbourhood in East Jerusalem, the section of the city captured by Israel in 1967 and claimed by the Palestinians as their capital.
The Popular Front for the Liberation of Palestine, a small militant group, said the cousins were among its members, though it did not say whether it had instructed them to carry out the attack.
Hamas, the militant Palestinian group that runs the Gaza Strip, praised the attack.