The US actor, 64, received high dose radiation and chemotherapy after a tumour was found at the base of his tongue in 2017.
In 2024, several years after his cancer treatment, he noticed his energy levels were depleting while he was filming in Italy for a TV show.
Appearing on David Tennant Does A Podcast With..., he said: "I would be so tired in the afternoon, like completely exhausted by one o'clock and I was like, something's wrong with me".
"Finally, when it was all over, or just before the last one (episode), I had a blood test and I was like, I know something's f****** wrong with me."
"My thyroid was non-functioning."
The thyroid is a small butterfly-shaped gland in the neck near the windpipe that produces hormones affecting heart rate and body temperature.
Having too much or too little of these hormones can cause symptoms that may need treatment.
"I was like, what is it? Is it stress?," he said
"I was like, I don't know what's happening, and they kept saying 'your cholesterol level's really high'.
"I was like, why? It doesn't make any f****** sense, and what happened was because I had radiation six, seven years ago, it burned out my thyroid."
Tucci said he was now taking medication to treat the problem.
"Because I still get (tired) in the afternoon ... literally you can't think, you can't move, you can't think and once I started taking the pill, it made a huge difference, but I want to get back to where I was," he said.
An underactive thyroid (hypothyroidism), where the gland does not produce enough hormones, can lead to tiredness, weight gain and sensitivity to the cold, which can be treated by the patient taking daily hormone tablets.
Damage to the thyroid during treatments for an overactive thyroid or thyroid cancer can cause hypothyroidism.
The actor, best known for appearing in the films The Devil Wears Prada and The Hunger Games, was widowed in 2009 when his wife Kathryn Spath died from breast cancer.
The Conclave star is now married to Felicity Blunt, sister of Tucci's The Devil Wears Prada co-star Emily Blunt.