Defense ministers from Djibouti, Ethiopia and Kenya were in Mogadishu on Tuesday to prepare for the summit, the information ministry statement said.
Restrictions will be imposed on the movement of people in Mogadishu for the summit, the government said, while flights in and out of Mogadishu are being suspended, according to aviation workers.
"Only emergency aircraft and those transporting VIPs will be allowed during those two days," said Hassan Yare, an employee with a commercial flight company.
Leaders of some of the nations in an African Union force involved in a major offensive against the insurgents "will closely discuss ways to jointly confront the dangers" posed by Al-Shabaab in the region, the Somali government said.
"This collaboration is expected to lead to the quick liberation of the country from the Kharijites (renegades) who have been dealt heavy blows on the battlefield in the past few weeks," it said, using a government term for Al-Shabab.
The army and local clan militias backed by the AU force known as ATMIS have been waging an operation against Al-Shabab in recent months, which has seen them recapture swathes of territory and several strategic towns from the jihadists.
After taking office in May last year, President Hassan Sheikh Mohamud declared "all-out war" on the Al-Qaeda linked group, which has been waging an insurgency in the troubled Horn of Africa nation for more than 15 years.
Although Al-Shabab fighters were forced out of the capital by African Union troops in 2011, they still control parts of the countryside and have carried out numerous attacks both in Somalia and in neighboring countries.
And they have frequently retaliated against the latest offensive with bloody strikes in the capital and elsewhere.
The 20,000-strong African Union force, formerly known as AMISOM, has a more offensive stance and mission than its predecessor.
Its goal is to gradually reduce troop numbers to zero by the end of 2024 with security to be assumed by Somalia's army and police.