But the new law has been opposed by employer groups who say businesses cannot afford to give women the time off, even though the second three months would be optional, unpaid leave.
"Doctors advise that mothers should breastfeed exclusively for six months. I want mothers to have this time," lawmaker Boniface Gatobu who proposed the legislation told the Thomson Reuters Foundation.
"The main motivation for this bill is the health of the mother and the child."
Kenya has high rates of child malnutrition. The 2014 Kenya Demographic and Health Survey (KDHS) found that 61 percent of children under six months were exclusively breastfed, a sharp increase from 32 percent five years earlier.
Last year business lobby groups unsuccessfully opposed proposals obliging companies to set aside breastfeeding areas with breast pumps and fridges for employees with infants.
Employers' representatives said the new bill would damage the career chances of young women in the workplace.
"If passed, the bill will hurt the chances of employment for women of child bearing age," said Jacqueline Mugo, executive director of the Federation of Kenya Employers.
"It is not that we do not understand that mothers need time with their children, but it is impractical," she said. "Our economy cannot sustain such time offs and the bill is counterproductive."
In Nairobi, 42-year-old secretary and mother of two Salome Nang'oni said she quit her first job because her boss told her to come back to work just seven weeks after she gave birth to her first child.
She said if passed, the new law would help women balance work and domestic life.
"We will get to have more time with our children and also be more comfortable while at work knowing that our young ones got the best possible start to their lives," she said. "It is such things that will also make employees loyal to their employers."
In March, India legislated to more than double maternity leave, extending fully paid leave to 26 weeks from 12 weeks and ensuring a work from home option for working mothers.
According to a 2013 report from the Pew Research Center, Estonia offered the most paid time off for parental leave, about two years. Hungary offers at least one and a half years of paid leave.