The Colombia goalkeeper underwent a scan after cutting his head in a collision with Udinese winger Ignacio Pussetto during the first half 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.
"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."
By the time Ospina had departed the field, Napoli had already conceded a two-goal lead with Seko Fofana and Kevin Lasagna levelling things up for Udinese at the break.
However, second-half goals from Dries Mertens and Arkadiusz Milik secured victory for Carlo Ancelotti’s side.
Next up for Napoli after the international break is a trip to play Claudio Ranieri’s Roma at the Stadio Olimpico on Sunday, March 31.
Ospina, who joined Arsenal from French side Nice in the summer of 2014, departed Emirates Stadium on a season-long loan deal last August.
He had asked new Gunners boss Unai Emery if he could be granted a temporary move after the arrival of Bernd Leno from Bayer Leverkusen had pushed him further down the pecking order.
The 30-year-old ‘keeper has started 21 times for Napoli since that move and has competed with Alex Meret, who replaced him against Udinese, for the number-one spot.
Napoli have the option to make Ospina’s move permanent at the end of the season.