MOSCOW—New-car sales in Russia last month plunged 38% over a year earlier, and auto-industry executives warned a weaker economy and declines in the ruble’s value mean the worst is yet to come.

“The market is entering a very difficult phase now, and February is only the beginning. Industry sentiment is the next few months will be extremely difficult, and the market bottom has yet to be found,” said Joerg Schreiber, chairman of the Association of European Business Automobile Manufacturers Committee, which compiles monthly sales...