His lawyers launched the court appeal to fend off the first lawsuit faced by the 77-year-old, since he lost his total immunity on abdicating last June.
Spain's Supreme Court last month agreed to examine the claim by Ingrid Sartiau, a Belgian housewife reportedly in her late 40s.
"Juan Carlos has lodged an appeal against the admission of the paternity suit," a judicial source told AFP on Saturday.
Sartiau herself has also launched an appeal since the court has not yet ordered Juan Carlos to undergo a DNA test as she demanded in her suit, the source added.
Lawyers on both sides and state prosecutors must now examine the appeals before they are sent to the court for a ruling, which could happen within weeks, the source said.
Sartiau claims Juan Carlos fathered her in the mid-1960s before he became king. He married Queen Sofia in 1962.
Juan Carlos took the throne in 1975 after the death of the dictator Francisco Franco and reigned for 39 years.
He handed the crown last year to his and Sofia's son Felipe VI, 47, hoping to freshen the monarchy's image.
The royal palace said on Saturday it would not comment on the case since it was a private matter.
Juan Carlos's last years on the throne saw the monarchy plunged into scandal, including a fraud investigation implicating his youngest daughter Cristina, 49.
A judge has ordered Cristina to stand trial in that case.
Juan Carlos also sparked outrage in 2012 for going on an elephant-hunting trip to Botswana at the height of Spain's economic crisis.