Research by the group found women who take time out to raise a family save an average of £15,000 less than those who do not take a break.
Women in full-time work throughout their careers save an average of £83,000 compared to £68,000 saved by those who take years out or switch to part-time hours to meet their childcare responsibilities.
The difference is even starker between men and women.
Male workers save an average of £114,000 during their career - 27% more than a female counterpart working full time.
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This jumps to a 40% difference in savings between the average man compared to a woman who takes time off to have a family.
Which? said that over the years with investment growth, the £2,000 cash injection will help close this gap.
Under its proposals, each household would be able to choose which parent or guardian's pension scheme the contribution is made to.
If no scheme were to be nominated, the sum would be made to an account with Nest - the auto-enrolment pension scheme set up by the Government.
Which? also wants to see a hike in minimum pension contributions from 8% to 12%, for middle-income earners - boosting pension pots by an average of £50,000.
It said the current 8% contribution should remain for those on lower incomes to avoid financial hardship, while others would be able to choose to switch down to the lower rate.
Jenny Ross, money editor at Which?, said: "Since its introduction, automatic enrolment has successfully drawn in millions of new savers to workplace pensions, but 'the motherhood penalty', which already impacts women's income, threatens to leave those who choose to work reduced hours due to childcare responsibilities significantly worse off in retirement.
"If the Government is committed to pension equality it should introduce a £2,000 pension contribution for first-time mothers, and also raise the minimum contribution rate for all middle-income earners to ensure they can retire with an adequate pension pot."
A spokeswoman for the Department for Work and Pensions said: "Under the new state pension, by 2030 we expect that more than three million women will be getting an average of around £550 more each year compared to the old system.
"Automatic enrolment (AE) has been an extraordinary success and truly revolutionary reform, bringing more than 10 million workers into workplace pension saving since 2012.
"And through AE, the proportion of women in the private sector without a workplace pension has been drastically cut, from 60% in 2012 to 20% in 2017.
"Current contribution rates have been deliberately phased-in to balance bringing people into saving with affordability for both savers and employers, and the recent increase to the minimum contribution rate will help people save more."
Gregg McClymont, director of policy at workplace pension provider The People's Pension, argued that affordable childcare is also vital to closing the pensions gap.
He said: "While many women choose to reduce their working hours or leave their job because they want to spend more time with their kids, the cost and availability of childcare is a key factor for some.
"If we're going to tackle pensions inequality, not only are changes to auto-enrolment required but better provision of affordable childcare is a must to enable those mums that want to keep working or work more hours, to be able to."