The incident prompted the UN to suspend its twice-weekly passenger flights to Tigray for humanitarian personnel, UN spokesman Stephane Dujarric said.
The strike – the fifth on Mekelle since Monday, according to the government – coincided with an intensification of fighting further south in Amhara region, as Ethiopia's nearly year-long conflict rumbles on.
Ethiopian Prime Minister Abiy Ahmed's spokeswoman Billene Seyoum told AFP the air force was targeting a training centre used by the Tigray People's Liberation Front rebel group.
She said this was “also serving as a battle network hub by the terrorist organisation".
Residents told AFP that the air strike hit a field, setting alight fodder collected for livestock.
According to reports from doctors and officials, 11 civilians were injured in the attack.
The UN flight forced back because of Friday's air strike was carrying 11 humanitarian staff, said Gemma Connell, head of the UN's humanitarian co-ordination office for Southern and Eastern Africa.
“I can confirm that the government was informed of that flight before it took off, and can also confirm that the flight was forced to turn back in mid-air, because of the events on the ground,” Ms Connell said.
TPLF spokesman Getachew Reda criticised the Ethiopian Air Force for putting the flight at risk.
“Our air defence units knew the UN plane was scheduled to land and it was due in large measure to their restraint it was not caught in a crossfire,” Mr Getachew said on Twitter.
Meanwhile, a civilian injured in an earlier strike being treated at Mekelle's Ayder Referral Hospital died from their injuries on Friday, research director Dr Hayelom Kebede said.
Mr Abiy's government has been locked in a war against the TPLF since last November.
Tigray itself has seen little combat since late June, when the rebels seized control of much of Ethiopia's northernmost region and government forces largely withdrew.
Escalating air campaign
On Monday, the Ethiopian Air Force launched two strikes on Mekelle that the UN said killed three children and wounded several other people.
And on Wednesday the government said it bombed TPLF weapons caches in Mekelle and the town of Agbe, 80 kilometres to the west.
A hospital official told AFP that Wednesday's strike in Mekelle injured at least eight people.
A fourth strike in Mekelle on Thursday did not result in any casualties, according to medics and the TPLF.
The international community has voiced alarm about the attacks.
A US State Department spokesman said on Wednesday that Washington “condemns the continuing escalation of violence, putting civilians in harm's way".
The air raids come amid reports of heavy fighting in Amhara, where the TPLF launched an offensive in July.
On Wednesday, Mr Getachew claimed rebel fighters had taken control of at least two towns in Amhara, putting the cities of Kombolcha and nearby Dessie – where tens of thousands have sought refuge from their advance – “within artillery range".
Much of northern Ethiopia is under a communications blackout and access for journalists is restricted, making battlefield claims difficult to verify independently.
Dessie residents on Thursday reported a heavy military presence in the area as displaced civilians from conflict-hit towns farther north continued to arrive.
On Thursday, the UN again warned about dire humanitarian conditions in Tigray, saying that some aid groups were forced to suspend food distribution for lack of fuel.
AFP has documented deaths from starvation in several parts of Tigray, based on internal documents from aid groups active there.
The UN said last week that the number of young children admitted to hospital due to severe malnutrition between February and August was double the number during the same period last year.
Some 2.5 per cent of screened children were diagnosed with severe malnutrition during the past week, the UN said Thursday – up from 2.3 per cent the week before.
Thursday's report also noted that during the week ending October 13, only 52,000 people in Tigray received food assistance – just 1 per cent of the 5.2 million that aid groups are targeting.
“To reach 5.2 million people with food assistance within a six-week cycle, partners are expected to assist at least 870,000 people on average per week,” the report said.