From July 1, Australian businesses will need to pay $US23 per tonne of carbon dioxide emitted.
The tax might also be applied to companies operating in the oil and gas fields in the Timor Sea, which are jointly shared by both countries.
The government in Dili says it is yet to receive formal details about the possibility of the additional costs from the Australian Government.
Researcher Charlie Scheiner, from the Timor-Leste Institute for Development Monitoring and Analysis, has told Radio Australia's Connect Asia program it is Canberra's responsibility to reach an agreement.
"If Australia intends to tax facilities in the JPDA they need to give some formal notice and have a discussion," he said.
"And I understand from Timor-Leste government officials that this issue has come up in the joint commission that resolves disputes under the Timor Sea Treaty but they haven't reached any resolution yet."
The Timor Sea Treaty provides for the sharing of profits from petroleum exploration in the JPDA (Joint Petroleum Development Area), an area that is subject to overlapping territorial claims by East Timor and Australia.
East Timor's Secretary of State for Natural Resources Alfredo Pires says his nation does not produce much pollution and it can't afford to be generous.
"We're very different in terms of our economical development and anything that gives any additional cost to this little country would be seen as unfair," he said.
"There are pros and cons in regards to this whole issue of climate change and carbon tax.
"But we will be very concerned about any additional costs that may be borne upon the country."
A spokeswoman for Australia's Climate Change Minister Greg Combet says officials from both nations have been discussing the potential impact of the tax.
She says the Australian Government will consult East Timor about the application of the price to the joint area.