The minister's action followed press reports in recent months that the highly-priced tree was being harvested indiscriminately and exported to Europe, the Middle East and Asia, especially India where sandalwood is widely used to manufacture expensive perfumes.
Mrs Meghji directed all institutions charged with protecting Tanzania's natural resources, including the Tanzania National Parks Authority (Tanapa), to intensify anti-poaching patrols in national parks where the tree is illegally harvested.
The minister also said stricter laws would be introduced to regulate trade in the tree, and ensure that only crude oil extracted from the tree can be exported.
The head of protection at Manyara National Park, Donat Mnyagatwa, said middlemen who have valid permits and licenses to export the tree's products have been sending poachers into the park to harvest the tree.
The tree fetches up to $15,000 per tonne. Hundreds of containers of all sizes are believed to have been shipped out in recent years.
Poaching of the tree in national parks follows its depletion in areas where harvesting is allowed by the Ministry of Natural Resources. However, the ministry only permits the cutting of the tree's trunk from selected forests and not the uprooting of the entire stem.
The ministry's guidelines have been largely ignored. Several cubic metres of the tree worth millions of shillings were intercepted last year in various places including inside national parks in Arusha and the surrounding townships.
Recently, four containers of the logs were impounded at Dar es Salaam port.
Mr Mnyagatwa said that sandalwood poachers gain entry into the park from Bugeri, Kansai and Ayalalio villages in Karatu, Arusha region, and Mayoka village in Manyara region. A number of people have been arrested and have either been given short sentences or fined.
Village leaders in Karatu had asked the government to limit exportation of the tree as it faces possible extinction, in parks.
An official at the Arusha Regional Forestry Secretariat confirmed that sandalwood is one of the 12 nationally protected trees. It was upgraded to the class A level of highly valued tree species last year to protect it from extinction.
"Despite government recognition of the need to protect the tree, smuggling now threatens its existence," he said adding, "It is a serious matter now that smugglers are harvesting it in national parks."
Apart from making perfumes, sandalwood is also an ingredient in lotions, soaps and candles. Mashed into a paste, it is also used in folk medicine and spread on the skin to purify the complexion and heal rashes.
Realising its value and the threat of its extinction, in 1792, the Sultan of Mysore, in India, declared sandalwood a royal tree. It continues to retain that status today and no one is allowed to own it even when it grows on private land.