Shabudin Yahaya from the ruling Barisan Nasional coalition said marriage could help victims "lead a better life".
Malaysia, a Muslim-majority country, has just passed a new law on sexual offences against children.
Despite opposition efforts, the law does not ban child marriages.
It remains legal for Muslims under 16 to get married in Malaysia under certain circumstances.
'Remedy to social problems'
Speaking during a parliamentary debate on the bill on Tuesday, Mr Shabudin said that although rape was considered a criminal offence, the rapist and the victim should both be "given a second chance to turn a new leaf".
"Perhaps through marriage they [the rape victim and rapist] can lead a healthier, better life. And the person who was raped will not necessarily have a bleak future.
"She will have a husband at least, and this could serve as a remedy to growing social problems," he said.
He also said some children were "physically and spiritually" ready for marriage.
"Some girls who are aged between 12 and 15 years have bodies like 18-year-old women," he said, citing his experience as a former Sharia court judge.
He later said his comments had been taken out of context, but that he opposed criminalising child marriages as they are a part of Islamic law, Reuters reports.
A 'worrying and dangerous trend'
In Malaysia, there has been an increasing emphasis on strict Islamic codes of conduct in recent years.
Sharmila Sekaran, chair of the Malaysia's Voice of the Children NGO, said the politician's words represented a "worrying trend" for young girls.
Child marriage in Malaysia
- The official legal marrying age for Muslims in Malaysia is 16 for girls and 18 for boys.
- But Muslim children younger than 16 can legally marry with permission from their parents and religious courts.
- A UN report estimates that more than 9,000 child marriages took place in Malaysia in the past five years.
- Most child marriages are believed to be in rural or traditional communities.
"You have politicians like him, giving voice to dangerous statements and backward views. It only serves to reinforce the view that rape is ok," Ms Sekaran told BBC News.
She described his argument that children could marry as "flawed and unsupported by any evidence".
"Sharia courts are full of divorces among young couples. There is a very, very high rate of divorce and re-marriage among couples in Malaysia."
Ms Sekaran, who was present in parliament on Tuesday, said most people there had been "outraged" by Mr Shabudin's remark.
Mr Shabudin's comments drew widespread criticism and anger from many Malaysians.
"His was a horribly backward and archaic view that should have no place in our modern society," wrote Joshua Hong in a Facebook post.
Lewynd Nishel wrote: "It's a sad day indeed when our society has degraded to a point where it's not only legal but socially acceptable to beat women and rape children."
"Rape is rape. To think that this man is an MP really disgusts me," said Farhan Akmal from Kuala Lumpur. "Get him out. Revoke his position. He isn't fit to lead."
The fact that Mr Shabudin is involved in the debate on the child sexual offences bill was not lost on his colleague Seri Abdul Rahman Dahlan, who said he was "shocked and disappointed".
"It is abhorrent in this 21st Century to suggest that a rapist, who should in the first place be prosecuted, have the means to escape legal responsibility simply by marrying his victim," he said in a press statement.
"Every child has the right to live, to dream, and to have fun... Our government and lawmakers have the responsibility to protect the best interest of Malaysian children."