Republican Gov. Jack Dalrymple has indicated he would sign the measures, the most restrictive in the nation, Fox News reported. The North Dakota House is expected to take up other abortion bills next week.
Sen. Margaret Sitte, R-Bismarck, was among the lawmakers who successfully pushed for passage.
"Is it right to discriminate against a human being based on his or her gender, based on his or her sexuality before that person is born?" KXMB-TV, Bismarck, quoted Sitte as saying, "and in our North Dakota Human Rights Act we say absolutely not."
Sen. Connie Triplett, D-Grand Forks, however, countered the bills infringe on women's rights.
"Now many of these abortion bills we have passed, the majority has attempted to control what happens to a woman's body," she said, "and that, Mr. president, in my mind, is an abomination, but this goes one step further, now you are attempting to control their mind."
The bill banning abortions once a heartbeat is detected would effective end the procedure after 5-6 weeks gestation. Arkansas last week passed a law banning abortions after 12 weeks gestation.