More than 19 people were also wounded in the strike that hit the hospital in Abs, in the rebel-held northern province of Hajja, the Paris-based aid agency said.
A Doctors Without Borders (MSF) staffer was among the dead, it said.
The hospital strike was the latest in a series of coalition raids that allegedly hit civilian facilities -- including a school on Saturday where 10 children were killed.
The coalition launched the bombing campaign in March last year after Shiite Huthi rebels seized large parts of Yemen, including the capital Sanaa.
It stepped up air strikes this month after UN-mediated peace talks between the rebels and Yemen's internationally-backed government were suspended.
MSF said Monday's attack was the fourth on one of its facilities in less than a year.
"Once again, a fully functional hospital full of patients and MSF national and international staff members, was bombed in a war that has shown no respect for medical facilities or patients," said Teresa Sancristoval of MSF's emergency unit in Yemen.
MSF said the GPS coordinates of the hospital "were repeatedly shared with all parties to the conflict, including the Saudi-led coalition, and its location was well-known".
- 'String of unlawful attacks' -
Key Saudi ally Washington raised concerns about the reports, with State Department spokeswoman Elizabeth Trudeau saying: "Strikes on humanitarian facilities, including hospitals, are particularly concerning."
UN Secretary General Ban Ki-moon went further, condemning the strike and saying he was "deeply disturbed" by the intensification of air raids in Yemen.
"Hospitals and medical personnel are explicitly protected under international humanitarian law and any attack directed against them, or against any civilian persons or infrastructure, is a serious violation of international humanitarian law," Ban said in a statement.
Amnesty International termed the bombardment as "deplorable", saying it "appears to be the latest in a string of unlawful attacks targeting hospitals, highlighting an alarming pattern of disregard for civilian life".
A Joint Incidents Assessment Team (JIAT), composed of members of the coalition, said it was aware of the reports and "has urgently launched an independent investigation".
It promised to publicly announce findings of the probe.
The 14-member JIAT was set up as a standing investigation team following mounting criticism of the civilian death toll from the bombing campaign.
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Earlier this month, it acknowledged "shortcomings" in two of eight cases it investigated of air strikes on civilian targets in Yemen.
In one of them, the team held the coalition responsible for hitting an MSF-run hospital but accused the rebels of having used the facility as a hideout.
- Rebels urge 'independent' probe -
The team is also investigating Saturday's strikes on the school in the rebels' northern stronghold of Saada.
The coalition said it bombed a training camp where the rebels were using child soldiers and not a school.
A recently formed rebel council governing from Sanaa called on the United Nations to form an "independent committee to investigate" the coalition "crimes".
The so-called Supreme Political Council condemned the hospital strike, blaming the international community whose "silence has encouraged the coalition... to commit further massacres".
The rebels formed the 10-member council late last month, in a move that put an end to the three months of peace talks in Kuwait.
A UN envoy has described the ruling body as a violation of commitments to the peace process.
Fresh coalition air strikes on Tuesday struck Abs, Saada and areas surrounding Sanaa, military sources and residents said.
The coalition resumed air strikes on Sanaa on August 9, almost three days after the talks were suspended, with one raid reported to have hit a food factory in the city during working hours, killing 14 people.
The resumption forced the closure of Sanaa airport, but its director Khalid al-Shayef said three flights landed on Tuesday.
Two were carrying World Food Programme (WFP) and Red Cross employees, while a Russian plane brought in humanitarian aid, he said.
The conflict has devastated already impoverished Yemen.
The UN says more than 6,400 people, mostly civilians, have been killed since March last year and more than 80 percent of the population is in need of humanitarian aid.
In the south, jihadists have exploited the conflict to expand but government forces, backed by the coalition, launched a weekend offensive to retake Abyan province.
Hundreds of soldiers deployed Tuesday in provincial capital Zinjibar and the neighbouring town of Jaar, a military source said.