The letter, issued by the Office of the Superintendent of Police on Sunday, threatens Tsundue with prosecution under the Foreigners Act of 1946 if he fails to obey the order.
When asked what prosecution would mean, the Additional Superintendent of Police, Santosh Patial, replied: "Deportation to Tibet," said a press release issued by Tsundue, who is general secretary of Friends of Tibet.
The pressure on Tsundue is the result of his high profile protests during the visits of Chinese Prime Ministers Zhu Rongji and Wen Jiabao in 2002 and 2005. Hu Jintao will visit India from November 20-23.
"This is an attack on the freedom of all Tibetans and people living in democratic India.
"I was born in India and I am working only nonviolently for the human rights and freedom of my people. This issue is not about me but it is about the six million Tibetans who are suffering every day under Chinese rule and who are deprived of their voice to speak out against the occupation."
Following the order, 11 policemen are following Tsundue around the clock and police have also taken up residence in the room next to his.
Hu Jintao will visit New Delhi, Agra and Mumbai from November 20-23 before leaving for Pakistan. While in New Delhi, he is expected to attend official functions at Vigyan Bhawan and Hyderabad House. In the lead up to Hu's India visit, government officials from both countries have been meeting to discuss trade and border issues.