The video featured 20 pregnant women and was produced by the Yad L'Olim organization, which helps immigrants and their families.
"My mother is also beautiful," one woman said in the video. "Now can she come for the birth?"
If pageant contestants were allowed to visit, women in the campaign argued that their parents should be as well, as they provided essential emotional and physical support before and after birth.
One pregnant immigrant from Mexico told the Yedioth Ahronoth daily she was currently alone as a result of the travel ban.
"I'm here alone, I don't have anyone to help me," she said. "Why can't my mom, who is fully vaccinated and has all the necessary papers, be able to come and be with me."
Although the Interior Ministry described the comparison to the Miss Universe contest as "misplaced", and said allowing parents into Israel could "pose a health risk", Minister Shaked asked the Health Ministry to examine the request.
The Health Ministry granted the request, with some caveats.
Non-Israeli parents of pregnant women must be fully vaccinated before flying. They can only visit if the pregnant woman does not have parents in Israel already and is due to give birth soon.
Founder and director of Yad L'Olim Dov Lipman thanked Minister for the decision. "Now all ministries must work together to make sure the allowance is granted to those who apply for it. I am also working with the authorities to address the issue of those who gave birth recently and are in need of support from their families."
Israel's ban will stay in place until at least December 13.
As of Monday, they have reported 21 cases of Omicron, 16 of which were from abroad.