The violent attack in Bahir Dar, capital of Amhara, was linked to the subsequent assassination of army chief Gen. Seare Mekonnen, who was shot dead by a bodyguard at his residence in Addis Ababa. His condition was unknown.
He said the attack followed a violent incident in the Amhara region, outside Addis Ababa, where soldiers allegedly led by a renegade brigadier raided a meeting of the regional government and killed officials including the region's president.
Prime Minister Abiy Ahmed's government faces growing pressure from regional strongmen, including in Amhara, a flashpoint in growing ethnic violence in Ethiopia.
Describing the circumstances of General Mekonnen's death, PM's press secretary Seyoum said that he was shot dead by his bodyguard just hours after an attempted coup in Amhara left the regional president and another top adviser dead.
Also, earlier reports came out from Bahir Dar, capital of the regional state, that there were some gunshots fired at the regional government's building and people were seen running for their lives. Within a few hours, all access to the Internet had been shut down and army and police checkpoints sprung up around the capital.
Ethnic violence, typically sparked by land disputes, has displaced almost three million people across Ethiopia.
Events scheduled for Sunday have been cancelled, state TV said.
Since coming to power past year, Abiy has tried to spearhead political reforms, to open up the once isolated, security-obsessed country of 100 million people on the Horn of Africa.
In other regions, dozens of people have been killed in the last few months in clashes between residents of northern Benishangul Gumuz and Amhara states. It is not known if he has been arrested, though many others involved in the plot have been apprehended.
Abiy has released political prisoners, removed bans on political parties and prosecuted officials accused of gross human rights abuses, but his government is battling mounting violence.
Ethnic bloodshed has flared up in many areas, including Amhara.
The US state department has warned its staff in Addis Ababa to stay inside. Shortly after his election in June previous year, militants from the Oromo Liberation Front threw grenades at a rally attended by Mr Abiy, killing two. Several opposition groups have called for the polls to be held on time despite the unrest and displacement.