The Oscar-winning actor, 64, underwent an MRI scan after the scare during the 15th Tashkent International Film Festival in Uzbekistan.
He became unwell while touring the Afrasiyab Museum in the ancient Silk Road city of Samarkand – and felt his “entire left arm go numb for about eight seconds”.
House of Cards star Spacey was taken to the Innova Diagnostic Clinic in the city to undergo a series of tests – including an MRI scan.
It was feared the actor could have suffered a heart attack, but doctors later gave him the all-clear.
A source close to the actor said: “Mr Spacey was taken to a medical centre over health concerns.
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“He was treated professionally by doctors and staff and found to have no problem with his heart.”
The Superman Returns star appeared on stage at the festival later that night, and told the crowd his health was “normal”.
Spacey said: “It made me really take a moment and think about how fragile life is – for all of us.”
The star, who won Oscars for his roles in The Usual Suspects and American Beauty, gave a speech at the festival’s closing ceremony on Monday.
He said: “I experienced something here today that was unexpected.”
The star went on: “I was looking at these extraordinary murals on the walls and I suddenly felt my entire left arm go numb for about eight seconds.
“I shook it off, but I immediately told the people I was with and we went immediately to the […] medical centre.”
He added: “I spent the afternoon there having a variety of tests. Staff took care of me, and even put me through an MRI.
“Everything turned out to be completely normal, and I’m grateful it’s not anything more serious.”
Spacey had the day before announced his “comeback” at an event in the capital Tashkent – insisting his “best roles were ahead of him”.
He was earlier this year cleared of a series of charges of sexual assault.
He is currently attempting to rebuild his career after losing out on major roles and being axed from Netflix’s House of Cards.
Speaking outside Southwark Crown Court in July, he told reporters in tears: ” I lost everything in a matter of days.”
Spacey broke down as he was cleared of sexually assaulting four men on charges dating back 22 years.
He had denied all charges – saying the allegations against him were motivated by “money, money and then money”.
Allegations by several men in the UK and US had already an impact on Spacey’s career.
He was stripped of an International Emmy Award and was edited out of Sir Ridley Scott’s film All The Money In The World.
His central character in the Netflix series House of Cards was also killed off after he was axed from the show.
In November last year, it emerged that a US arbitrator ordered Spacey to repay nearly £24.6million to the studio that made the hit show.