Sevilla star Joan Jordan was hit on the head by the object while Nabil Fekir was celebrating Betis' equaliser at the Estadio Benito Villamarin.
The 27-year-old fell to the ground and received medical attention, but was able to walk off the pitch.
Referee Ricardo de Burgos Bengoetxea was seen handling the object, which was reportedly a metal pole.
The last-16 tie was then abandoned, and will be restarted on Sunday behind closed doors on the 39th minute, with the score at 1-1.
A statement from the RFEF, Spain's FA, read: "The Copa del Rey round of 16 match between Real Betis and Sevilla FC is suspended. The RFEF condemns any act of violence on the playing fields."
Sevilla released a strong statement condemning the actions and gave an update on the condition of Jordan.
A club statement read: "Sevilla FC would like to convey all its affection to Joan Jordan, who fortunately, and this is undoubtedly the only important thing, is at home after being hit by an object thrown from the home stand during the derby.
"Joan left the Benito Villamarín dazed and was taken to hospital, where he was examined and underwent a series of tests required by the protocol due to the concussion. The final diagnosis is cranioencephalic trauma and the player will be kept under home observation until a minimum period of 24 hours has passed without any alarming symptoms.
"Sevilla FC condemns the violent act suffered today by Joan Jordan, an unacceptable act in the world of sport committed by an individual who, of course, does not represent the fans of Real Betis or the way of living football in our city.
"Likewise, the club demands the utmost respect for Joan Jordan, a true professional and an exemplary person who has suffered an appalling attack."