National state broadcaster NHK reported that 19 people have died and 45 were injured - of which four are in a serious condition.
Armed police encircled the centre which offers support to people with disabilities, including providing creative and rehabilitation activities.
NHK said the suspect, 26, is a former employee at the facility, Tsukui Yamayuri-en. He has been arrested on suspicion of attempted murder.
Television footage showed a number of ambulances parked outside the facility, with medics and other rescue workers running in and out.
Kyodo News agency initially reported that 19 people were killed and 20 injured, but later said at least 15 people were dead and 28 injured.
Police did not immediately release an official death toll, but it is the worst mass stabbing in Japan in recent years.
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Sagamihara is home to a large US Army depot called the Sagami Army Depot.
The attack comes after Mayu Tomita, a Japanese pop star, was left in a coma in May when a fan stabbed her dozens of times after she allegedly turned down a gift he had sent her.
Listen: Newstalk ZB's Chris Lynch on the Tokyo knife attack
Police later recovered a 8cm knife from the crime scene in western Tokyo. A bloodstained mask and a trail of blood were also found on a set of stairs near to where the star had been due to perform a concert.
Tomohiro Iwazaki, 27, later confessed to stabbing Tomita in the neck and chest.
He claimed he "ambushed" the star because she returned a gift he sent her.
In March last year, five people were also stabbed to death in a knife attack on a Japanese island.
A man was arrested after the victims were discovered in two houses.
Media reports said those killed range in age from 60 to 80 and lived in homes set among farms in the city of Sumoto on Awaji Island.