It said normal production may not return until the end of the year.
Honda will significantly cut production of the new 2012 Civic, the sixth most popular car in the U.S., through the summer, if not longer.
In addition, the 2012 version of the CR-V small SUV will be delayed by at least a month this fall. To make up for shortages, Honda will keep making the 2011 version.
Both vehicles are made in North America, but like other automakers, Honda must cut production because it's running low on Japanese imports of chips, sensors and other parts. Japanese plants that supply them were damaged by the March 11 earthquake or hampered by power outages.
Nearly every major auto company has had to idle factories due to shortages. Honda, Toyota Motor Corp. and Nissan Motor Co. have been hit particularly hard. Supply companies are scrambling to build their parts elsewhere, but setting up alternate factories takes months.
"Our goal remains to normalize overall production sometime around the end of the year," John Mendel, executive vice president of sales for American Honda, wrote in the dealer memo.
Shortages also will cut supply of some Acuras, Honda's luxury cars. Dealers won't be able to order the TSX small car and wagon and the RL large sedan until later in the year, the memo said.
The shortages come at a time when gasoline in the U.S. is hitting $4 a gallon in 13 states. That normally drives up sales of fuel-efficient models from Honda and Toyota.
Honda spokeswoman Christina Ra conceded that the production cuts could send some buyers to other brands, but she said some buyers might be willing to wait.
"We can certainly beef up production once things get back to normal," she said.
Honda sold nearly 67,000 Civics through March, up 21 percent from last year. Sales of the CR-V, which ranks No. 11 in U.S. sales, were up 58 percent to just over 57,000 through March.
Some industry analysts think production cuts by Japanese automakers could help General Motors, Ford, Chrysler, Hyundai and other automakers that have not been hit as hard by parts shortages.
GM, Ford and Hyundai have far better entries in the compact car market than in past years, and buyers who would automatically have bought a Honda or Toyota may end up trying other brands.
Mendel's memo said Honda would have to stop taking orders for some paint colors due to lack of a certain shiny pigment made only in Japan. Ra said the colors are types of red, blue, dark gray and white.
Last month Honda said it would slow down production at its 10 U.S. and Canadian auto factories into at least early May because of shortages. The company still says none of its 21,000 North American factory workers will be laid off. Toyota has made similar moves in North America.
Separately, a Toyota engine factory in Huntsville, Ala., remains closed for lack of electricity. Alabama was devastated by tornadoes on Wednesday, and company spokesman Mike Goss said Toyota isn't sure when the plant will reopen.
The plant makes engines for the Tundra and Tacoma pickups, and the Sequoia SUV.
Goss said factories that assemble the trucks have not been affected so far. The pickups are made in San Antonio, Texas, while the Sequoia is made in Princeton, Ind.