Authorities also arrested eight suspected attackers, police spokesperson Paul Manka said on Thursday.
The first major arrests of women for the veil ban have been carried out in the capital, N'djamena, since Wednesday in line with "anti-terrorism" measures, he said.
Chadian authorities banned wearing full veils in public places in June to prevent suicide attacks, especially by the Nigerian armed group Boko Haram.
The group used women and children to carry out five suicide bombings in a village near Lake Chad on Saturday, killing at least 36 people.
Police also arrested eight suspected attackers in the operation, Manka said.
The women will be released after paying a 100 000 CFA ($170) fine, he said, adding that if they are repeatedly arrested they will be charged with complicity with attackers.
Muslim-majority Chad banned the full-face veil, ramped up security measures and bombed Boko Haram positions in Nigeria in June after the first ever attack by the armed group in its capital.
Boko Haram has used dozens of girls and women in recent suicide bombings in Nigeria, Chad, Cameroon and Niger, raising fears it is using kidnap victims to target countries that have pledged to contribute to a regional force to combat the group.
Boko Haram's six-year-old fight has left an estimated 20 000 people dead as it seeks to carve out an Islamic state in northeastern Nigeria, according to Amnesty International.