Customers have been left without phone or internet access, while one city's air raid sirens stopped working.
Kyivstar's chief executive implied Russia could be responsible.
The Kyivstar network is estimated to have some 24 million mobile customers and a million home internet users.
Reports emerged on Tuesday morning that people and businesses had lost mobile and internet signal.
Air raid sirens in the north-eastern city of Sumy also malfunctioned as a result of the outage.
Military authorities in the area announced they would send out police and emergency vehicles to alert residents of any incoming missile or drone strikes.
An investigation has been opened by the Security Service of Ukraine.
The company's general director, Oleksandr Komarov, also appeared to suggest Russian actors could be to blame.
The operator said no-one's personal data had been compromised.
Russia launched a full-scale invasion of Ukraine in February 2022, with the war now well into its second year.
Separately, Ukraine's military intelligence claimed to have carried out a cyber-attack on Russia's federal tax system in recent days.
It said Russian efforts to restore services were now into their fourth day.
This Cyber News was published on www.bbc.com. Publication date: Wed, 13 Dec 2023 01:29:05 +0000