The Colombia goalkeeper underwent a scan after cutting his head in a collision with Udinese winger Ignacio Pussetto at Stadio San Paolo.
Ospina, who is on loan at the Serie A side from Arsenal, received treatment on the pitch and initially played on before collapsing just prior to half-time.
The 30-year-old spent the night under observation and Napoli confirmed further tests came back clear.
Ospina has withdrawn from his country's upcoming friendlies against Japan and South Korea as a precaution.
"David Ospina was this afternoon discharged from the clinic where he had been admitted last night for a series of investigations and specialist visits," read a Napoli statement.
"All tests are negative. The visits [ruled out] any problems.
"The player has been advised to have a few days off and will not respond to the call-up of his national team."