She urged the public to be careful and responsible in their opinions and comments concerning the judiciary due to the wide repercussions of their actions.
"It must be recognised that unfounded and baseless criticisms against the judiciary would weaken the administration of justice and erode the confidence of the public reposed in this important institution," she said when speaking at a ceremony held in honour of her appointment as the 16th Chief Justice in the Federal Court room.
She said if there were allegations of misconduct on the part of judges, parties with information should lodge their reports with the relevant authorities so that proper investigations may be carried out.
"The public may also write to me, the President of the Court of Appeal or the Chief Judges of the two respective High Courts, for us to do the needful,” she said.
Tengku Maimun said it is a disservice to the judiciary and the country as a whole, if one were to continue making wild allegations, especially in the social media without resorting to the proper channel for the allegations to be effectively addressed," she said.
She said judges do not respond to criticisms and allegations but speak through their judgments.
"This tradition which was intended to preserve impartiality and respect for our courts, prevents a judge from getting into public debates with unhappy litigants or dissatisfied critics," she said.
She said to protect the integrity of the judiciary, appropriate action has been and will be taken against those who tarnish the image and dignity of the judiciary.
She also said the judiciary respects and values the public right to comment on a judge's work but criticism of a judge's decision should be done responsibly and based on the facts.
Tengku Maimun also said in deciding cases, judges are answerable to no one, except their conscience and their learning, where decisions were made solely on the evidence presented in court by the parties and in accordance with law.
She said the public tend to equate justice with judgment in favour of the poor over the rich, the weak over the strong, the rakyat or the opposition over the government.
"That certainly is not the yardstick for justice. A wrong is a wrong regardless of whether it is committed by the rich or the poor, the weak or the strong, the rakyat or the opposition, or the government," she said.
On her appointment, Tengku Maimun said it was a privilege and a great honour to be appointed the first woman Chief Justice of Malaysia.
She pledged her commitment to defend the rule of law and independence of the judiciary.
Tengku Maimun appeared choked up (sebak) when she said she would discharge her duties and she would continue to heed the message of Surah An' Nisa verse 58 and Surah An-Nisa: verse 135 of the Quran.
Among those present in the ceremony were the Dewan Negara Yang di-Pertua Tan Sri SA. Vigneswaran, Speaker of Dewan Rakyat Datuk Mohamad Ariff Md Yusoff, Attorney-General Tommy Thomas, Malaysian Bar president Datuk Abdul Fareed Abdul Ghafur, president of the Sabah Law Society Brenndon Keith Soh and president of the Advocates Association of Sarawak Ranbir Singh Sangha.