The girl said during a TV interview the child would be "like having a doll".
Experts criticised Mr Pinera's comments as having no scientific foundation.
Mr Pinera supports Chile's abortion laws, which outlaw the practice in all circumstances. His critics want it legalised in cases of rape, and want the girl to be allowed an abortion.
The 11-year-old girl appeared in a TV interview on Monday, saying: "I'm going to love the baby very much, even though it comes from that man who hurt me.
"It will be like having a doll in my arms."
The girl was raped repeatedly over a two-year period by her mother's boyfriend, who has since been arrested.
Mr Pinera said he had asked the health minister to personally look after the girl's health.
"She surprised us all with words showing depth and maturity when she said that, despite the pain caused by the man who raped her, she wanted to have and take care of her baby," he said.
Forensic psychologist Giorgio Agostini said the girl would not have the mental or emotional capacity to understand her situation.
Sources: World Health Organization, Guttmacher Institute
"What the president is saying doesn't get close to the psychological truth of an 11-year-old-girl," he told the Associated Press news agency.
"It's a subjective view that is not based on any scientific reasoning."
The girl's case has already sparked a public debate about abortion.
Campaigners argue that the laws, which date back to the authoritarian rule of Gen Augusto Pinochet, should be changed to allow for abortions in cases of rape or when the mother's health is at risk.
Michelle Bachelet, the likely presidential candidate next year for the left-leaning opposition, supports the campaign.
Ms Bachelet earlier commented that the 11-year-old girl need to be protected.
"I think a therapeutic abortion, in this case because of rape, would be in order," she said.
Chile is one of seven Latin American countries where abortion is completely banned.
Last month, the case of a seriously ill woman in El Salvador made international headlines when the courts upheld the ban on abortion even though the woman's life was at risk and the foetus was unlikely to survive.
She was eventually allowed to have a caesarean section.
Chilean President Sebastian Pinera has praised as "brave and mature" a pregnant 11-year-old rape victim who said she was happy to have the child.