Rights groups question the legality of that proclamation, which U.S. Customs and Border Protection spokesman Ralph DeSio said was issued to deter illegal crossings.
At least one person in Mexico was seen helping adult members of the family group over the top of the wall, and then dropping the children to the waiting family members below, according to the release.
The child that suffered a facial injury was treated by border patrol agents, according to CBP.
"Frustrated" members of the Central American "migrant caravan" began "breaching" the US-Mexican border this week; jumping a ten-foot tall fence in a last-ditch effort to reach the United States before returning to their country of origin.
"Since that caravan formed in mid-October, we've seen 90,000 people come to our border, 85 percent of those crossing illegally between ports of entry, and all lured by the fact that our legal framework has huge gaps that create the opportunity to stay in the USA while awaiting a court hearing, even if they don't have a lawful permission or protection claim".
Reuters reported that other migrants managed to squeeze through the fence on the beach.
She was arrested with her 20-year-old husband and 2-year-old son.
The inhospitable conditions have increased the apparent frustration of thousands of the caravaners, some of whom arrived at this Mexican border city two weeks ago.
Ninety minutes later, she and her family were over the fence.
He has sent troops to the border and issued an order denying the possibility of asylum to migrants crossing the southern border illegally - but that order has since been halted by a U.S. federal judge.
Last week city authorities bussed them to a concert venue that now acts as a federally run shelter, 14 miles to the south.
Meanwhile, thousands of migrants remain in Tijuana, with only a few trickling through the border, and Mayor Juan Manuel Gastélum told Fox News the city can't keep supporting the migrants.
"In those six hours that the border was closed, we lost approximately 129 million pesos", he said, referring to recent clashes at the border.