Sinha, 66, left for Australia last night, saying he was "embarrassed" over the controversy surrounding his July ruling. He also denied claims by the government that he was sick.
"I am the guardian of the judiciary, in the interest of the judiciary I am leaving temporarily so that its image does not get hurt. I will return," he said ahead of his departure for Australia.
He also rejected an earlier claim by Law Minister Anisul Huq about his sickness while his leave application to President Abdul Hamid was being processed.
"I am not sick, I am well... I am not fleeing either," the chief justice told newsmen in front of his official residence while on his way to the airport.
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He also issued a written statement, in first such media interaction since the government announced his one-month "sick leave" beginning October 3.
The government row with the higher judiciary sparked in July this year when the apex court delivered a verdict declaring void the 16th constitutional amendment, scrapping parliament's authority in impeaching Supreme Court judges.
The dispute grew in the subsequent weeks as several senior government leaders virtually attacked Sinha over his comments, blasting the government for its reaction and gave Pakistan's example where ousted Prime Minister Nawaz Sharif was stripped of his premiership under an apex court ruling.
Main Opposition outside parliament Bangladesh Nationalist Party of ex-premier Khaleda Zia has supported Sinha, saying the government was trying to control the higher judiciary by launching a campaign against the apex court judgment.
Hours ahead of his departure, BNP Secretary General Mirza Fakhrul Islam Alamgir said that the government forced Sinha to go abroad to "establish its full control over the judiciary".
Sinha, Bangladeshs first Hindu chief justice whose tenure expires in January 2018, in his written statement said he was a "bit worried about the independence of the judiciary".
He complained that the judge who became the acting chief justice to perform the "routine" job in his absence was encouraged by the government to bring changes to the Supreme Court administration soon.
"If any interference is made in the chief justice's administration, it can be easily assumed that the government is interfering in the higher court and this will further deteriorate the relationship between the judiciary and the government. It would not bring any good to the state," he concluded.
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