Russian prosecutors have issued warnings to Western companies in Russia, threatening to arrest corporate leaders there who criticize the government or to seize assets of companies that withdraw from the country, according to people familiar with the matter.

Prosecutors delivered the warnings in the past week to companies including McDonald’s Corp. MCD 2.19% , International Business Machines Corp. IBM -0.31% and KFC owner Yum Brands Inc., YUM 0.38% the people said. The calls and visits included threats to sue the companies and seize assets including trademarks, the people said…

The warnings have prompted at least one of the targeted companies to limit communications between its Russian business and the rest of the company, out of concern that emails or text messages among colleagues may be intercepted, one of the people said. Other companies have moved to transfer executives out of Russia, another one of the people said.