The charges are linked to an article which said the country's Prime Minister, Mahathir Mohammed, had conspired against his former deputy, Anwar Ibrahim, who is now serving a prison sentence for corruption.
Zulkifli Sulong, editor of the newspaper of the opposition Parti Islam SeMalaysia, denied the allegations.
But his co-defendant, Chea Lim Thye, the newspaper's printer, pleaded guilty and was fined 4,000 ringgit ($1,053) by a Kuala Lumpur court.
Mr Zulkifli was one of four senior opposition figures arrested in January in an operation that provoked strong international condemnation.
They included, Marina Yusoff, vice-president of the Keadilan party, whose sedition trial also began on Monday.
Amnesty International has said the use of the Sedition Act against government critics threatens "to strike at the heart of free speech".
The Hakarah newspaper article was written by Chandra Muzaffar, deputy president of the Keadilan party, which is headed by Anwar's wife, Wan Azizah Wan Ismail.
He said it was "shameful that elements in the police force, the attorney general's office, courts and media are willing to be made tools in the biggest conspiracy planned by the prime minister and his allies".
Plot
Mr Chandra was referring to the trial and imprisonment of former deputy prime minister Anwar.
Anwar was jailed for six years for corruption in April 1999 and is currently on trial for sodomy, a charge he denies.
He says he is the victim of a political plot to drive him from power.
Mr Zulkifli's trial was postponed until Thursday.
The authorities have already limited Harakah to two editions a month - a decision its publishers plan to take to the courts as politically motivated.
Race riots
In a separate trial in the northern state of Penang, Ms Marina was charged over a speech she made last September in which she reportedly accused ruling party leaders of provoking the 1969 race riots.
The anti-Chinese riots, in which more than 200 people died, are a highly sensitive topic in Malaysia.
The Sedition Act, which has been denounced by rights groups, prohibits any speech that might "bring [the government] into hatred or contempt or excite disaffection".
Also arrested in January were Anwar's lawyer, Karpal Singh, who is to stand trial for sedition in July, and his former aide, Mohamad Ezam Mohamad Nor, who is charged under the Official Secrets Act.