The whale, which is about 10m (33ft) in length, was washed up at Shingle Street, near Hollesley shortly after 15:00 BST on Sunday.
The Zoological Society of London (ZSL) said it was a juvenile fin whale and that a post-mortem examination would be carried out on Tuesday.
Suffolk Police warned people to stay clear of the carcass, which has been tied down.
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Rob Deaville, manager of the cetacean stranding investigation programme for ZSL, said fin whales were a "fairly unusual species to be found beached in the UK".
He said that last year, out of 600 strandings in the country, only about five would have been fin whales.
"Looking at photos, it does look a little bit on the thin side, so starvation may be a factor but we have an open mind," he said.
Andrew Capell, of HM Coastguard Search and Rescue, said: "We answered the call and we originally thought it would be a porpoise, because we tend to get them quite a bit.
"But we arrived on the beach to find this rather handsome animal.
"There are a few grazes on it where it has been on the shingle, but there is no other wounds or injuries.
"There's a lot of interest today as it is not the sort of thing you see in Suffolk."
A crew from Aldeburgh Lifeboat station was also called to Shingle Street.
Coxswain Steven Saint said: "Unfortunately it had already died when the crew were there - but there were reports it had been in the water a short time before."
Another whale died after being stranded at a beach in Bridlington, east Yorkshire, on Sunday.

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Efimova, who was allowed to compete after appealing against a doping ban, took silver with Tutton fourth.
"I would've preferred it to have been a completely clean Games," the 20-year-old Welsh swimmer said afterwards.
"I couldn't help who was here. I'm not happy with it, but that's how it is."
Rie Kaneto won Japan's seventh gold medal at Rio 2016 to beat Efimova into silver.
China's Jinglin Shi won bronze, just six one-hundreths of a second ahead of fourth-placed Tutton.
Her British team-mate Molly Renshaw, 20, finished sixth.
"Being fourth is a bit gutting, no matter who is in front of you," Tutton added.
"It's a great experience and I'm a bit disappointed to come fourth. I'm so close to a medal and that would have been a dream.
"But just to get into the final is a great experience that I'll take on with me for years to come."
"It was a bit gutting but it will make me tough in the long run and it just makes me more hungry for a medal so hopefully next time I'll get closer."
Efimova, who said she was tired of answering questions about her doping past, defended her right to compete at Rio.
She was banned for 16 months in 2013 after traces of an anabolic steroid were found in her system.
Earlier this year she was given a provisional ban after testing positive for meldonium, but the International Swimming Federation lifted the suspension after advice from the World Anti-Doping Agency (Wada).
The Court of Arbitration for Sport (Cas) has ruled that athletes cannot be banned from Rio on the basis that they have been previously sanctioned.
"Cas considered my appeal and I won. If someone dislikes it and has a different opinion, they can go to CAS," she explained.
"I am not for doping and I have never used it. The second case was completely not my fault. Everyone should have a second chance. When you drive and you are just issued a ticket, no-one puts you in jail."
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Earlier, Ben Proud set a British record to reach the men's 50m freestyle final.
Commonwealth champion Proud, 21, swam a time of 21.54 seconds to qualify fifth fastest for Friday's final (02:44 BST Saturday).
Find out how to get into swimming with our special guide.
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A whale has died after beaching on a shingle bank off the Suffolk coast.
[NEXT_CONCEPT]
Great Britain's Chloe Tutton appeared to criticise controversial swimmer Yulia Efimova's presence in Rio after the Russian finished ahead of her in the 200m breaststroke.