Mumbai: The high court in August said the ban “violated the constitution” and was discriminatory towards women.
The ban was imposed in 2012 – the trust said it was a “sin” to allow women to touch the tombs of male saints.
Women’s activists campaigning to enter the shrine have described Monday’s development as a “huge victory”.
“We are grateful the courts are standing by us in our fight against the patriarchal attitudes of men running religious shrines,” Zakia Soman of the rights group Bharatiya Muslim Mahila Andolan (BMMA), which has challenged the ban on women entering the 15th Century shrine in the court, told the BBC.
Although women were allowed into the compound and other parts of the Haji Ali mosque, the 2012 ban barred them from entering the inner sanctum which housed the tomb of a Sufi saint.
Many Islamic mosques belonging to the Shia and Sunni sects also allow women inside, though many keep them in clearly demarcated areas.
India women fight to enter temples
In recent months, India has seen a number of campaigns to allow women into religious shrines that bar their entry.
Activists – both Hindu and Muslim – have dragged patriarchal managements of shrines to courts all across India.
On Monday, the Haji Ali shrine trust told the court that it would allow women to enter the shrine within a month.
Ms Soman said the trust should not have challenged the high court order in the Supreme Court since “their stand to keep women out is not tenable – legally or morally”.
Most Sufi shrines across the country, and globally, allow women into the sanctum, and until the ban, they were allowed to touch the tomb of the saint at Haji Ali, Ms Soman says.