Emergency service crews attended to the incident involving a KLM aircraft that arrived in Glasgow from Amsterdam this morning.
The aircraft operator confirmed the dry ice used to package glass tubes containing vaccines had started to leak, prompting passengers on board KL1473 to be evacuated about 10am.
There are reports the vaccine involved was for polio.
An exclusion zone was put in place around the plane as a precaution.
KLM said passengers were "never in danger".
Passengers were subject to a three-hour wait while the plane was cleaned and the suspected contamination was checked.
The incident was stood down at 1:30pm after the package was declared "safe" by emergency crews.
A statement from KLM said: "KLM confirms that on board KL1473, operating between Amsterdam and Glasgow, a package packed in dry ice started to leak.
"The package contained glass tubes with vaccines. These tubes have remained intact with only the cooling around them starting to leak.
"As a precaution, the fire brigade cordoned off the immediate vicinity of the aircraft. Passengers were never in danger, but were taken off board as a precaution.
"The incident was stood down at 1:30pm after the package was declared safe by emergency services."
At least 20 firefighters are reported to have been in attendance, alongside ambulance crews and police.
The exit slip to Glasgow Airport reopened just before 1pm after being initially closed due to the incident.
The alarm was raised while cargo was being offloaded from the aircraft, which was parked at a stand adjacent to the international pier of the terminal.
A spokesperson for Glasgow Airport said: “At approximately 10am today, the airport fire service attended an arriving KLM flight in response to concerns raised over a piece of cargo.
"The incident was stood down at 1:25pm after the package was declared safe by emergency services.”
The airport said part of the international pier, where passengers embark and disembark from aircraft, was also evacuated as a precaution.
It said the rest of the airport had been operating normally during the incident, with no flights cancelled.
One person in the terminal, known only as Louise, posted on Twitter: "Waiting at Glasgow airport, have been evacuated off plane and staff now giving out water and people being escorted in groups of 8 to use the toilet on the plane."