Manquillo suffered the injury during his side's 2-0 Copa del Rey defeat to Real Madrid, a result that gave Carlo Ancelotti's side a 5-0 aggregate win in the semi-final.
The 19-year-old was forced from the field in the 44th minute following a heavy collision with Cristiano Ronaldo.
Manquillo landed awkwardly after an aerial battle with the Portugal international, landing on his face and placing considerable pressure on his neck and back.
Atletico released a statement on Wednesday that confirmed a CT scan would rule him out of football for "four to six weeks".
They also said that a "fracture of foil of C7 vertebra without displacement" would see him remain in hospital until Thursday.
Manquillo has not been a regular for Atletico this season, making just seven appearances in all competitions.
