The baby girl, who was given the name of Princesa by Red Cross workers, was found soaked, shaking and with a 38.5C temperature in one of the 94 inflatable boats that reached the Spanish coast on Tuesday, Spanish media reported.
While she was shared the boat with other would-be immigrants, including children, her parents were not aboard the vessel.
"We took care of the girl while she was here, a nurse gave her a check up and volunteers stayed with her, giving her bottled milk," Red Cross spokesperson Miguel Domingo told The Local from southern Spain.
"These are similar to the procedures we follow with all babies who arrive here after being rescued at sea, because their mothers arrive on shore very tired. The only difference in this case, of course, was our volunteers had to stay with the baby girl at all times."
"The baby had a slight fever, but this cleared up quickly," he added.
The toy in which 'Princesa' was found had departed from Morocco before being intercepted en route to Tarifa, Spain's southernmost port.
According to other rescued African immigrants, an altercation with Morrocan police officers before the tiny boat's departure prevented the parents from making it onto the inflatable boat with their child.
The government of the Spanish region of Andalucia has taken custody of Princesa and is now hoping her parents will contact them.
She has been temporarily placed with a family, regional authorities said on Friday.
Spain's coast guard picked up more than a thousand sub-Saharan migrants in the Strait of Gibraltar on Tuesday and Wednesday, part of a surge of migrants crossing the Mediterranean to reach Europe's southern shores.
Authorities blamed the rise in the number of migrants trying to cross the Strait on traffickers seeking to take advantage of calm summer seas and the end of the Islamic holy Ramadan month of fasting on July 28th
On Thursday, Morrocco and Spain agreed to step up efforts to stop the flow of immigrants, with Spain's interior ministry saying it would send 475 agents to Spain's African enclaves of Ceuta, Melilla and to the southern Spanish port of Algeciras.
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