Under Texas law, a license can be suspended if the holder is indicted on felony charges, reports the Houston Chronicle.
DeLay's license was suspended by a county justice of the peace, a decision that has been appealed.
DeLay, a strong supporter of gun rights, also had faced election law indictments, which were later dismissed, but not the money laundering indictment.
Separately, Jerry Patterson, who originally wrote the Texas law regarding the suspicion of gun-carrying rights, now thinks the law should be removed, saying since its passage legislators have amended it and removed some of the parts he called "onerous," the Chronicle reported.
"There is a presumption of innocence. Would we take away his First Amendment right to free speech?" Patterson was quoted as saying.