The Qatar-owned store has been combing its customer database, singling out those with a Russian phone number or who have said they live in the country.
An email sent by the store to one wealthy Russian, which has been seen by The Telegraph, said: "As you may be aware, the UK authorities have introduced further regulations as part of their ongoing sanctions against Russia which specifically target the sale of luxury goods.
"The regulations seek to prohibit the supply of many categories of luxury goods over certain values (generally £300) to individuals who are either currently or ordinarily in Russia."
The letter includes a link to the new regulations and encouraged the customer to "review them".
It said: "To comply with these regulations, Harrods has been required to review its customer information to identify those customers who it appears (by reference to the country or phone number information they have provided to us) might currently or usually be resident in Russia.
"Based on this information, we have identified you as someone who might currently or ordinarily be resident in Russia. If this is correct, this would mean that you are subject to the regulations and we will be unable to supply you with any restricted luxury goods."
The department store has declined to say how its business might be affected by any ban.
It is perhaps not surprising it appears keen to enforce the letter of the sanctions regulations after being heavily criticised in March for continuing to sell expensive Russian vodka after the invasion of Ukraine. It admitted "mistakenly" selling Beluga vodka, bottles of which were offered at more than £100.
However, its decision to limit purchases to impose the £300 limit is likely to spark accusations of discrimination from Russians affected.
Last month, Russian influencers posted videos online of them cutting up their Chanel handbags after being barred from making new purchases by the couture brand.
Harrods said in a statement: "In order to ensure we are complying with these restrictions, we reviewed our database to identify potentially impacted customers, and asked them to notify Harrods if the information we hold is not accurate and current. This was not based on nationality, but address/contact details or previous transaction delivery data.
"Our priority is to comply with regulations, informing potentially impacted customers on how it may limit their ability to shop at Harrods, and ensuring wider customers are not unduly affected. We are happy that we have been able to take this action and support customers in making them aware of recent government regulations."