By Agence France-Presse
Abe vowed to enhance pressure on the nuclear-armed state as tensions spike over Pyongyang's weapons development ambitions.
"Their outrageous act of firing a missile over our country is an unprecedented, serious and grave threat and greatly damages regional peace and security," he told reporters in Tokyo.
"We have protested to North Korea."
Calling for an emergency meeting of the UN Security Council, he said Japan would "strongly call for increased pressure on North Korea in cooperation with the international community".
South Korea's Joint Chiefs of Staff said in a statement that Tuesday's missile was launched at around 2057 GMT Monday from Sunan, near Pyongyang, and travelled east "and over Japan".
Japan on Tuesday deployed a Patriot Advanced Capability-3 (PAC-3) missile defence system at a US military base in Tokyo as part of a previously scheduled drill.
Tokyo has been on edge over North Korean launches since a mid-range ballistic missile flew without warning over the northern part of the country and into the western Pacific in 1998.
A decade later, in 2009, a North Korean projectile passed over Japanese territory without incident, triggering Tokyo's immediate denouncement.
At the time North Korea said it was launching a telecommunications satellite, but Washington, Seoul and Tokyo believed Pyongyang was testing an ICBM.