Zazou, a thoroughbred worth some $20,000 (£17,000), disappeared between Friday evening and Saturday morning.
Zazou is reportedly one of two of Mr Kadyrov’s horses that are still stabled in the Czech Republic.
The horses were placed under sanctions, following Russia’s illegal annexation of Crimea from Ukraine in 2014.
Ramzan Kadyrov is a strong ally of Vladimir Putin, although he has recently criticised Russian military leadership over the war in Ukraine. This is despite his own soldiers frequently being mocked on social media over TikTok videos which appear to have been staged.
Last year, Czech Radio reported that the Chechen leader’s stable of racehorses had been registered with the Czech Jockey Club organisation since 2012.
Zazou went missing from the Darhorse stud farm near Roudnice nad Labem, 50km (31 miles) north of the capital, Prague, police said.
The statement said a chain securing the sliding doors to the stable had been removed and the horse led away, presumably under cover of darkness.
They appealed to the public for any information on Zazou’s whereabouts, saying the 16-year-old bay had a distinctive irregular white star on his forehead.
Czech Radio reported that there was an attempt to remove the two horses – Zazou and a second thoroughbred named after Russian composer Mikhail Glinka – in January last year, weeks before Russia’s invasion of Ukraine.
Two Russian-speaking men arrived at the stud farm claiming they were under instruction to take the horses to Poland, arguing that sanctioned animals could be moved across borders as long as they did not leave the EU.
The stud farm’s owner was unmoved and locked the stables to prevent the horses being taken. He says the pair spent five days sitting in a van parked outside the gates, before finally leaving with a horsebox bearing Mr Kadyrov’s personal livery.
Under European Union sanctions, any prize money from races was to go towards the horses’ upkeep, but the rest has been frozen – a move that has enraged Mr Kadyrov.
“What can we say about human rights in the West, if they crudely violate the rights of horses, the most peaceful, kind and gentle animals in the world?” Mr Kadyrov asked on his Facebook page, in comments reported by the Moscow Times.