The women, some of whom have been held since Sunday, had been planning to make the Muslim Hajj pilgrimage to Mecca, only to be detained at airports in Jeddah and Medina.
There has been an understanding in the past that Nigerian women are exempt from travelling with a male relative – a requirement for women on the Hajj.
Nigerian diplomats say the agreement between National Hajj Commission of Nigeria and the Saudi authorities allows visas to be issued for Nigerian women going to Mecca as long as they are accompanied by their local Hajj committee officials.
Correspondents say many Nigerians have entered Saudi Arabia illegally to seek work.
Nigeria’s ambassador to Saudi Arabia, Abubakar Shehu Bunu told the BBC that authorities began stopping women under the age of 35 as of Sunday.
Sheu Bunu lodged a formal protest on Wednesday with the foreign affairs office in the Saudi capital of Riyadh.
“They are stopping women particularly between the ages of 25 and 35 without a male relative,” he told the BBC’s Hausa Service. “Those over 45 are not a concern to the Saudi authorities.”
One woman told the BBC her group was being held in Jeddah not because the women were travelling without male relatives, but because the surnames on their passports did not correspond with those of their husbands.
“Our husbands’ names are different from our surnames and they won’t allow that,” Bilkisu Nasidi, who travelled from the northern Nigerian city of Katsina, told the BBC’s “Focus on Africa” program.
She said the hundreds of women were sleeping on the floor, did not have their belongings and were sharing four toilets at the King Abdulaziz International Airport in Jeddah.
It is a common practice for Muslim women in Nigeria not to take their husband’s name.
More than two million Muslims are due to converge on Mecca for this year’s Hajj, which is set to culminate over a four-day period between October 24-29, depending on lunar observations.