It is unclear how the laboratory FarmaQuimica Sur, a supplier of active ingredients and pharmaceuticals based in the southern city of Malaga, made the mistake.
The sudden hair growth caused by the contaminated batches stops when children stop taking the drug, according to El Pais.
The babies were given tainted omeprazole, used to treat acid reflux and indigestion, as part of a formula.
A health ministry spokesman told AFP that 17 children had so far been affected in the northern region of Cantabria, Andalusia in the south and Valencia in the east.
Another mother, who did not disclose her name, said that it was distressing visiting multiple doctors trying to find a solution to her three-month-old son's condition.
Parents have been told the symptoms should improve in a matter of weeks and the excess hair will fall out.More news: Carli Lloyd received offer to kick in National Football League preseason game, trainer says
More news: NYT's Bret Stephens quits Twitter after spat over 'bedbug' insult
More news: Ruth Davidson to stay on as MSP for Edinburgh Central
Granada Hoy also said that health bosses have confirmed the drug was infected at its original source.
Although the children will recover from the condition, one mother has said it has taken an emotional toll on her daughter.
Angela Selles, a mother from Granada said her son, Uriel, was diagnosed at six-months old and was left with the "eyebrows of a grown man".
The only now available treatment for forms of the condition not related to drugs is removing the hair, including by shaving, waxing or performing laser removal on the area.
Some people have hair growth in a localized area.
Hypertrichosis is a common side effect of minoxidil and causes excessive hair growth all over the body.
It is a very rare condition which patients are either born with or develop later in life. Though the condition was mapped to a particular chromosome in a Mexican family, "the underlying genetic defect remains unknown", according to a study published in the American Journal of Human Genetics in 2011. "Being hairy makes me special", Sasuphan told Guinness.