Tenerife and Andorra were drawing 2-2 seven minutes into stoppage time when the incident occurred.
Owono ran towards the centre circle to clear a long ball when his knee appeared to collide with De Miguel.
The striker lay motionless on the pitch as medical staff treated him before he was taken by ambulance from Tenerife’s Estadio Heliodoro Rodriguez Lopez to hospital.
Players from both teams were visibly distressed by the incident, with a number of De Miguel’s team-mates in tears.
The referee showed Owono a straight red card before abandoning the match.
Spanish media, including Marca, reported De Miguel suffered a cardiac arrest in the ambulance and was resuscitated by paramedics on the way to hospital.
Andorra, Tenerife’s opponents on Monday, said: “With broken hearts and devastated, we want to send our most sincere condolences to the family of Jesus de Miguel, to all his team-mates, friends, and to CD Tenerife.”
Former Barcelona defender Gerard Pique, who co-owns Andorra, said: “I am sorry with all my soul. Rest in peace, Jesus.”
De Miguel’s former club, Castellon, said: “It’s hard to find words when reality strikes in such an unfair way.
“We join with all our affection in the grief of his family and loved ones, whom we embrace in these terribly difficult moments and to whom we extend our most heartfelt condolences.”
Javier Tebas, president of La Liga, said: “Today, we all share the terrible pain of an irreparable loss.
“My deepest condolences to his family, loved ones, team-mates and the whole club.”
Real Madrid and France striker Kylian Mbappe wrote on his social media: “Much sadness, there are no words.”
The Spanish football federation announced following De Miguel’s death that Tuesday’s Spanish Cup fixtures had been postponed.
Two fixtures in the first round of the men’s Copa del Rey were due to be played, while Espanyol were set to take on AS Celtas in the women’s Copa del Reina competition.