Abdisamad Gallan said a boat said to have come from Yemen delivered sealed sacks full of land mines and artillery.
Correspondents say this is one of the biggest seizures of al-Shabab weapons.
The discovery was made after a tip-off from residents in Qandala, a coastal town in the semi-autonomous region of Puntland, Mr Gallan said.
The al-Shabab group says it wants to strengthen its presence in Puntland.
The al-Qaeda-aligned group once dominated all of central and southern Somalia, but has now lost all the major towns it once controlled, although it still occupies many rural areas.
Somalia descended into a patchwork of territories controlled by rival warlords and clans after the overthrow of President Siad Barre in 1991.
Puntland became autonomous in 1998 and has remained mainly free of the Islamists’ influence, but is known for its pirate bases.
Mr Gallan, the governor of Puntland’s Bari province, said it was believed that the boat had travelled from Yemen.
The crew escaped on their boat before they could be questioned, but Qandala residents said they were foreigners, he told the BBC’s Somali service.
Earlier this week, an al-Shabab website, Amiirnuur, said the militants were expanding their activities into Puntland and intended to show its residents the true path of Islam.
The group follows the Saudi-inspired Wahhabi version of Islam, while most Somalis are Sufis.
The website said Sheikh Abdur Kadir Mumim, an al-Shabab leader in Puntland, wanted to oust the region’s President Abdirahman Farole, who he accused of being against Islam as he had invited Nato officers into the region “to fight terrorists”.
Earlier this year, a UN report noted that al-Shabab was expanding operations further north, with an armed group in the region joining the Islamists.
The African Union (AU) troops fighting alongside Somali government army have been leading the fight against al-Shabab in southern Somalia.
The group was driven from the capital, Mogadishu, more than a year ago – and although the Islamists still launch occasional suicide attacks – correspondents say the city is experiencing a renaissance, with businesses opening and buildings being reconstructed.
There has also been progress on the political front with the election by MPs of a new president last month.