The government last week said the situation in northern Rakhine had stabilised and that it had ended a four-month security crackdown on Rohingya Muslims.
The security operation had been under way since nine policemen were killed in attacks on security posts near the Bangladesh border on October 9. Almost 69,000 Rohingyas have since fled to Bangladesh, according to UN estimates.
The United Nations has said the security crackdown may amount to crimes against humanity and possibly ethnic cleansing.
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Two soldiers were wounded in a five-minute clash with an armed group on the border with Bangladesh on Friday afternoon, the State Counselor's said in a statement late on Saturday.
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The screengrab of a recent YouTube video shows Ata Ullah, the alleged spokesperson of Saudi-backed Rohingya militant group Harakah al-Yaqin that took credit for the October 9 attacks Dhaka Tribune
"The forces providing security forces to workers preparing border fence between the Mile Post 56 and 57 in Buthidaung township were attacked by about 30 unidentified armed men in black uniforms positioned on hills in Bangladeshi side," the statement said, adding the armed men withdrew after security forces returned fire.
The security forces were still gathering information to identify how many members from the armed group were injured or killed during the clash, the office said in the short statement.
Bangladesh Border Guard could not immediately be contacted.
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Myanmar State Counsellor's Office and military did not immediately respond to requests for comments.
Myanmar's government blamed Rohingyas supported by foreign militants for the October 9 attacks on police, but has issued scant information about the assailants it called "terrorists".
A group of Rohingya Muslims involved in the October attacks is headed by people with links to Saudi Arabia and Pakistan, the International Crisis Group said in a report last year.
The government, led by Nobel laureate Aung San Suu Kyi, has denied almost all allegations of human rights abuses in Rakhine, including mass killings and gang rapes of Rohingya Muslims, and said the operation was a lawful counterinsurgency campaign.
The violence has renewed international criticism that the Myanmar leader has done too little to help members of the Muslim minority, many live in apartheid-like conditions in northwestern Myanmar.
Rohingya Muslims have faced discrimination in Myanmar for generations. They are regarded as illegal immigrants from Bangladesh and many entitled only to limited rights.