Puntland’s Security Minister, Khalif Isse, said Abdikafi Mohamed Ali was wounded in a raid at a militant safe house in the port city of Bossaso.
A soldier was killed in the operation and the city is in lockdown as the hunt continues for other militants, he said.
Al-Shabab, an al-Qaeda affiliate, has strong links with pirates in the area.
Analysts say piracy is a valuable source of funding for the Islamist group, which still controls smaller towns and rural areas of much of southern and central Somalia.
In the semi-autonomous region of Puntland, the militants have a base in Galagala, a mountainous and forested area to the west of Bossaso.
More al-Shabab fighters reportedly moved to Puntland towards the end of last year after losing some key footholds in the south, including the port of Kismayo, to the Somali army and an 18,000-strong African Union force.
Search for militants
Mr Isse told the BBC Somali service that Mr Ali was the head of operations for al-Shabab in Puntland.
His whereabouts were only discovered on Tuesday – and he was captured after a shoot-out, the minister said.
His identity was revealed on Wednesday when the suspect was paraded before journalists in Bossaso, Mr Isse said.
No traffic was being allowed in or out of Bossaso as the security forces searched for other militants believed to be in hiding in the city, the minister added.
Over the last few years, many opponents of al-Shabab in the region – including government officials, judges, security officers, religious leaders and scholars – have been assassinated.
Somalia has been hit by numerous conflicts since the overthrow of long-serving ruler Siad Barre in 1991.
Puntland declared itself an autonomous state in August 1998 as clan-warfare engulfed southern Somalia.
With the establishment of a new UN-backed government in Mogadishu last year, Puntland has said it is ready to be part of a federal Somalia.