The mobile service's problems started in the early afternoon and were gradually being fixed, according to SoftBank Corp. spokesman Naomasa Suzuki.
He said they were caused by a mechanical problem in Softbank's 4G telecommunications systems. In some cases, the 3G network services automatically kicked in.
SoftBank is a top cell-service provider in Japan, with some 40 million users.
The disruptions quickly became one of the trending topics on social media, and it was a major news items on public broadcaster NHK TV.
Some Japanese on Twitter said they were worried by no-signal notifications on their mobile phones and found the glitch inconvenient.
Fixed line services were not affected.
Softbank's shares are set to begin trading Dec. 19, with the price to be set on Dec. 10.
Founded in 1986, the carrier was the first to offer the Apple iPhone in Japan.
The chief executive of the parent company SoftBank Group, Masayoshi Son, was in the spotlight recently for his relations with the Saudi prince after the killing of Saudi journalist Jamal Khashoggi.
Son, who has denounced the killing, has been partnering with Saudi Arabian Crown Prince Mohammed bin Salman and about half of his $100 billion Vision Fund, established in 2016, comes from the kingdom. The fund has been investing in various companies, solar projects and artificial intelligence.
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