Colonel Cyrus Oguna said the attack was part of a push by an African Union (AU) force to capture the city.
Residents told the BBC that al-Shabab was reinforcing its positions in the city and people had started to flee.
AU forces have vowed to capture Kismayo – a port city that is key to financing and arming the al-Qaeda affiliate.
The move on Kismayo comes as Somali MPs prepare to choose a new president under a UN-brokered peace plan.
The election is due on 10 September.
‘Lucrative charcoal trade’
Kismayo residents said the port area was shelled twice and the airport three times.
Al-Shabab was testing its weapons and mounting guns on battle wagons, the residents said.
Some residents were fleeing, either towards the capital, Mogadishu, or the border with Kenya, amidst fears that a big battle could take place, they added.
Last month, al-Shabab lost control of Merca, the third biggest port city after Mogadishu and Kismayo, to AU and pro-Somali government forces.
In June, Kenyan Prime Minister Raila Odinga appealed to the US and EU to give financial aid for a “final onslaught” on Kismayo.
Kenya sent troops to Somalia last year, saying that it wanted al-Shabab defeated because the militants threatened its security.
Kenyan soldiers have since joined the AU force in the country, boosting its numbers to nearly 18,000.
Al-Shabab, which is affiliated to al-Qaeda, withdrew from Mogadishu last year after heavy fighting with AU and Somali government forces.
But it still controls many areas in southern and central Somalia.
In July, a UN report said the export of charcoal from Kismayo and Merca helped al-Shabab generate millions of dollars – despite a UN Security Council ban on countries buying charcoal from Somalia.
The report accused the United Arab Emirates and Saudi Arabia of failing to uphold the ban.
The total trade volume of charcoal exports from southern Somalia in 2011 increased to between nine million and 10 million sacks, generating revenues for the al-Qaeda group in excess of $25m (£16m), the investigators found, it said.