Asked what lines of inquiry police were pursuing, interior ministry spokesman Artem Shevchenko said: "It is one of three things: Murder, suicide or negligent handling of a weapon."
Mr Tymchuk was a former naval officer who came to national prominence in 2014 with his blogging on Russia's annexation of Crimea and the conflict in eastern Ukraine.
In particular, he set up the Information Resistance blog, which seeks to expose Russian military involvement in the ongoing conflict.
He was elected to parliament in October 2014 as a member of then-Prime Minister Arseniy Yatsenyuk's People's Front party.
A strange death
By Zhanna Bezpiatchuk, BBC News
At the high point of the conflict in Eastern Ukraine, Dmytro Tymchuk was one of the main newsmakers for Ukrainians.
In the information vacuum, chaos and panic of the war that had just broken out, he positioned himself as an independent military analyst with his own intelligence sources and access to leaks.
But actually his role was seen by many as that of a person who said out loud what Ukrainian officials could not for diplomatic and other reasons.
Journalists often referred to Tymchuk as a person who was able to explain what was really going on on the battlegrounds of the hybrid war from the Ukrainian viewpoint.
He came out with the toughest criticism of Russia and always blamed it for this war. Once he was elected to the parliament, he switched to legislative work.
Given he was a newsmaker during the war who knew a lot, his strange death raises concerns and suspicions in Ukraine.