Photos from Ukraine's State Emergency Service showed the hotel heavily damaged and firefighters at the scene.
Governor Oleh Synehubov said the injured included Turkish journalists. Two S-300 missiles struck at about 22:30 (20:30 GMT), he said.
Russia has stepped up air strikes on Ukrainian cities in the past two weeks.
Ukrainian officials say dozens of civilians have died in those attacks from drones and missiles.
Kharkiv, just 30km (19 miles) from the Russian border, has suffered extensive damage from Russian air strikes since President Vladimir Putin launched his full-scale invasion of Ukraine in February 2022.
In the latest strike, nine injured were taken to hospital, including a 35-year-old man in a serious condition, the governor said on the Telegram messaging service.
The city's mayor, Ihor Terekhov, quoted by Ukraine's Unian news agency, said "there were no military at all" in the hotel at the time, but 30 civilians were there. It is in the city's central Kyiv district. He said several homes and cars nearby were also damaged.
The Russian city of Belgorod, 74km north of Kharkiv, was hit by Ukrainian missiles and drones on 30 December which Russian officials say killed 25 civilians.
Russia has started moving hundreds of Belgorod children to holiday camps further away from Ukraine for three-week stays. A camp in Voronezh region received 93 on Wednesday and later 280 arrived in Kaluga region, state TV reported, adding that teachers would join them there.
President Volodymyr Zelensky, on a visit to Lithuania on Wednesday, urged Western allies to provide more air defence weapons. The Baltic nation is among the staunchest allies of Ukraine in bolstering Kyiv's resistance to the Russian forces.
"Air defence systems are what we lack the most. The fight against drones. I am happy that we have agreements with Lithuania and many other partners," he said in Vilnius. Lithuania and its two Baltic neighbours, Latvia and Estonia, are ex-Soviet states now in the Nato alliance.
In terms of GDP, Lithuania is the biggest donor of military aid to Ukraine, Germany's Kiel Institute for the World Economy reports. The US contribution to Ukraine's defence is, however, by far the largest.
Mr Zelensky, quoted by Interfax-Ukraine, said Vladimir Putin "will not calm down until he destroys Ukraine".
"He wants to fully occupy us. And sometimes our partners' doubts over financial and military assistance to Ukraine, quick reaction, gives courage and strength to the Russian Federation."
He said the Russian leader "won't finish this [war], until we all finish him together" and warned that the Baltic states and Moldova "may be next".
In recent days, the Ukrainian leader has held intensive talks with Western allies aimed at maintaining vital arms deliveries. Kyiv's counter-offensive late last year made little progress, and some in the West have questioned Kyiv's strategy, fuelling concern about the cost of the war.
With Russia now committed to much higher military expenditure, Nato countries are struggling to boost production of artillery shells and other heavy weapons.
An EU aid package worth €50bn (£43bn; $55bn) for Ukraine is stuck because of a Hungarian veto, while the divided US Congress has stalled over a new tranche of military aid.
After a video conference with the Ukrainian government on Wednesday, Nato said it had plans to provide "billions of euros of further capabilities" to Ukraine this year.
"Nato strongly condemns Russian missile and drone attacks on Ukrainian civilians, including with weapons from North Korea and Iran," Nato Secretary General Jens Stoltenberg said.
By Laurence Peter
BBC News