The incident happened following the Falcons' 31-23 road win over the Carolina Panthers, when Smith felt pain on the team's charter, according to NFL Network's Albert Breer. He was escorted off the plane and from there was taken to the hospital. Smith did not suffer a heart attack.
"All is fine," general manager Thomas Dimitroff said in a text message to Breer.
The Falcons later issued a statement.
"Following the Falcons game vs. Carolina today, head coach Mike Smith was transported to a hospital in Charlotte for a non-emergency matter," the team said. "Coach Smith is resting comfortably, his tests reaffirmed his health, and he is expected to be in Atlanta on Monday. The Falcons will provide further information as it becomes available."
With Smith clearing all tests after being hospitalized, team owner Arthur Blank sent his private jet to Charlotte to transport Smith back to Atlanta, a team spokesman told NFL.com's Steve Wyche. Smith was expected to land in Atlanta around 3 a.m. ET.