Gov. Mike Huckabee's office said that it accepted W.R. "Bud" Harper's apology and resignation.
"The forwarded e-mail was neither humorous nor acceptable," Huckabee said.
"In spite of all best intentions and dedication, we sometimes make mistakes," Harper, 72, said in his resignation letter. "Some of these mistakes are so simple that it seems unreal that they can carry us into a situation I must now address."
Harper said earlier that he received the verse, titled "Illegal Poem," from someone else and sent it along because he found it humorous.
Among the poem's lines: "Welfare checks, they make you wealthy, Medicaid it keep you healthy." Another line accuses immigrants of bilking the system: "By and by, I got plenty of money, Thanks to you American dummy."
A copy of the poem was obtained Tuesday by The Associated Press. Asked about it, Harper initially said he found nothing wrong.
"It was just a poem that I got that I thought was funny and you know how you exchange things with people," he said.
"I believe in a strong work ethic. Aside from that I have no statement, cause or agenda," Harper said.
"Whoever got concerned about this really had to reach to find something. I am very sensitive to people and I care about people. There was no intention ... to create any hard feelings."
Bob Trevino, director of Arkansas' chapter of the League of United Latin American Citizens and Huckabee's liaison to the Hispanic community, said the poem was an insult.
"We are not a drain on our community, we add value to our community. I would say to Bud Harper or anyone else out there, 'Show me how we are a drain on the public rolls,"' Trevino said. "In our culture if you don't work, you don't eat."
Huckabee appointed Harper, a former judge, in 1997, praising his work in handling the devastation from a 1996 tornado that killed six people and caused millions of dollars of damage in the Fort Smith area.