Kibrom Gebreselassie, chief executive of Ayder General Hospital, tweeted that an area near Mekele General Hospital had been hit late on Tuesday.
The extent of damage and casualties was unclear.
Getachew Reda, the TPLF spokesperson, said on Twitter that at least three bombs had been dropped and that the Mekelle hospital was among the targets.
Another doctor at Ayder confirmed to Reuters he had heard three explosions late at night.
On Tuesday, the TPLF said an offensive had been broken and a counter-offensive launched. He underscored the devastation in the region, which has not had banking, phone or electricity services for more than a year.
Fuel restrictions have also limited aid distribution, while patients are dying for lack of medicine and equipment.
Restoring services is a key demand of the TPLF before peace talks. The government wants talks to begin without conditions.
Reuters was unable to reach people in Mekelle for confirmation because the region has not had phone communication since Ethiopian troops pulled out more than a year ago.
The latest strike follows a hit on a children's play area on Friday that killed seven people, including women and children.
On Saturday, the Ethiopian government communication service said it had pulled its forces out of the town of Kobo, in the Amhara region bordering Tigray, blaming the TPLF for sending "human waves" against the town and endangering civilians.
The government said Tigrayan forces were attacking in two directions - along the border with Amhara to the south and along the border with Afar to the east.
Ethiopian government spokesperson Legesse Tulu, military spokesperson Colonel Getnet Adane and the prime minister's spokesperson Billene Seyoum did not respond to requests for comment.
At war since late 2020, the Tigray People's Liberation Front (TPLF), which controls the region, and Prime Minister Abiy Ahmed's central government have blamed each other for renewed conflict that is disrupting desperately-needed food aid.