The former Andhra Pradesh chief minister has recently joined microblogging site Twitter.
"Rahul Gandhi's reaction to the ordinance is dubious. He would have known about it every step from drafting to passage by the government," he said in another tweet.
Meanwhile, Naidu wrote a letter to President Pranab Mukherjee requesting him to direct the Centre to suspend the proposed ordinance till the subject matter was discussed in Parliament and public in detail before a final decision was taken on the issue.
"I strongly feel that approval of the ordinance was not expected from a person of your stature, which would only ensure perpetuation of criminals in politics."
"Such matters relating to the country's future ought to have been subjected to a national debate before simply allowing such backdoor public policies," the leader of opposition noted in the letter.
Gandhi on Friday called the ordinance to protect convicted MPs and MLAs from immediate disqualification as "complete nonsense".