The coalition said an investigation and examination of drone wreckage confirmed Houthi involvement in planning and carrying out Tuesday's attack.
It said the station supplies electricity to the Prophet's Mosque, one of Islam's holiest sites.
A Houthi military source, quoted by the Houthi-run Saba news agency, denied the accusation, calling it a "lie" and saying it was intended to cover up what he described as Saudi Arabia's failure to substantiate its earlier accusation that the Houthis targeted the Muslim holy city of Mecca.
Saudi Arabia said two weeks ago it had intercepted and destroyed a Houthi drone south of Mecca before it entered restricted airspace over the city.
The coalition described that incident as the second Houthi attempt to target Mecca since 2017 while the Houthis denied targeting Mecca or any other Islamic holy site.
The coalition said the Medina attack was part of what it described as repeated Houthi attempts to target the Two Holy Mosques and "provoke" Muslims worldwide.
It said it would continue taking measures to protect the holy sites and pilgrims.
The latest escalation is the most serious fighting between Saudi Arabia and the Iran-aligned Houthis since a United Nations-brokered truce largely halted cross-border attacks in 2022.
Hostilities resumed this year after the Houthis declared a naval blockade on Saudi Arabia in July and began attacking Saudi territory and shipping while Houthi forces also made major territorial gains along Yemen's Red Sea coast.
Saudi Arabia has responded with air strikes in Yemen and backed government forces fighting to push back the Houthi rebels.
