The ministry's online newspaper "September 26" reported on Tuesday that the clashes took place in the town of Moudia in Abyan province, where militants recently seized large areas and entire towns.
The report says four other militants were wounded during Monday's fighting. It identified the arrested leader as Abdel-Ilah al-Zahiri.
Security has collapsed across much of Yemen during its nine-month anti-regime uprising, allowing militants to take advantage of the turmoil to expand their reach.
Critics accuse Yemen's leader of 33 years, Ali Abdullah Saleh, of turning a blind eye to the militants' growing strength.
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