CARACAS, Venezuela—The largest private Venezuelan company and producer of 80% of the beer consumed here began to shut down its last beer plant on Friday, the latest deprivation in a country crippled by shortages.

After Empresas Polar SA closed its three other beer plants over the past several days, the shutting of the San Joaquin plant, near Valencia, will leave just a week’s supply of beer, the company said. Like many other firms here, Polar blames the government, which hasn’t allocated the dollars the company needs to pay...