Tigrai Television, controlled by the regional authorities, blamed the strike on Friday in Mekelle on the federal government.
No other military aircraft are known to operate in Ethiopian airspace.
The Ethiopian government subsequently urged residents of Tigray to stay away from military and training facilities, saying in an online statement that it intended to "take actions to target the military forces".
Federal government spokesman Legesse Tulu and military spokesman Colonel Getnet Adane did not respond to Reuters queries regarding the air strike, which happened days after fighting resumed between Ethopia's government and Tigray forces on the border of the Tigray and Amhara regions.
Kibrom Gebreselassie, the chief executive of Ayder Hospital, said the strike had hit a children's playground.
It was not immediately clear if there were any military facilities nearby.
He displayed images of the wounded and dead.
Tigrai Television showed images of damaged buildings and what appeared to be wounded people lying on the ground being attended by medical personnel.
A humanitarian source in the city confirmed hearing an explosion and anti-aircraft gunfire.
Kibrom said on Twitter that the hospital had received four dead from the strike, two of them children, and nine others were admitted with wounds.
Reuters could not independently verify his account.
Both sides have blamed each other for breaking a four-month-old ceasefire between Prime Minister Abiy Ahmed's government and the Tigray People's Liberation Front (TPLF), the party that controls Tigray.
War erupted in Tigray in November 2020 and spread to the neighbouring regions of Afar and Amhara a year ago.
Last November, Tigrayan forces marched towards Addis Ababa but were driven back by a government offensive that month.
A ceasefire was announced in March after both sides fought to a bloody stalemate and the government declared a humanitarian truce, allowing badly needed food aid into the region.
The fighting has displaced millions of people, pushed parts of Tigray into famine conditions and killed thousands of civilians.
The vast majority of residents of Tigray have had no access to telephone or internet service for more than a year.
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