DENVER — Money was pouring into Bruce Nassau’s five Colorado marijuana shops when his accountant called with the bad news: The 2014 tax season was approaching, and Mr. Nassau could not rely on the galaxy of deductions that other businesses use to reduce their tax bills. He was going to owe the Internal Revenue Service a small fortune.

“I had to write a check for $275,000,” Mr. Nassau said. “Unbelievable.”

The country’s rapidly growing marijuana industry has a tax problem. Even as more states embrace legal marijuana, shops say they are being forced to pay crippling federal income taxes because of a decades-old law aimed at preventing drug dealers from claiming their smuggling costs and couriers as business expenses on their tax returns.

Congress passed that law in 1982 after a cocaine and methamphetamine dealer in Minneapolis who had been jailed on drug charges went to tax court to argue that the money he spent on travel, phone calls, packaging and even a small scale should be considered tax write-offs. The provision, still enforced by the I.R.S., bans all tax credits and deductions from “the illegal trafficking in drugs.”

Marijuana business owners say it prevents them from deducting their rent, employee salaries or utility bills, forcing them to pay taxes on a far larger amount of income than non-marijuana businesses with the same earnings and costs. They also say the taxes, which apply to medical and recreational sellers alike, are stunting their hiring, or even threatening to drive them out of business.