In a written statement on Wednesday, Kaya, who is also a deputy from Istanbul province, said he will not vote in favor of the bill.
"While my sense of Turkish nationalism orders my mind and conscience to vote No to the bill on constitutional change, it also prevents me from hypocrisy," he said in the statement.
He said his resignation reflected his own personal views.
The new constitutional reform bill will be debated in the parliament on Dec.9.
Kaya's remarks came after MHP Leader Devlet Bahceli's statement on Tuesday that he would back the bill in the parliament.
The move -- the first open commitment to support the bill by the MHP leader -- brings a potential change to a presidential system one step closer.
Responding to journalists’ questions after Tuesday's MHP parliamentary group meeting in Ankara, Bahceli said: "I will give a Yes vote to the new constitutional bill and I will repeat it in the referendum."
However, it is not clear if all MHP lawmakers will follow their leader's move. The party has seen internal divisions since Turkey's November 2015 general election which saw it fall to fourth place in parliament.
The Turkish government has said it would put the constitutional changes to a referendum, even if the proposals gained enough support from lawmakers to pass through parliament.
The constitutional bill needs 330 votes to pave the way for a referendum.
The ruling Justice and Development (AK) Party has 316 seats and the MHP has 40 seats in the parliament.
Constitutional change -- in particular, the call for a presidential system -- has been on the political agenda since Recep Tayyip Erdogan, the former prime minister and AK Party leader, was elected Turkey's president in August 2014.
That election was the first time a Turkish head of state was directly chosen by popular vote.
In the current parliamentary model, the Turkish electorate votes for 550 lawmakers. A government is formed by a minimum number of 276 members of parliament.
In the proposed presidential system, the electorate would vote for a person to form a government independently of parliament, with no need for a vote of confidence.
Two other opposition groups in parliament -- the People’s Republican Party (CHP) and Peoples’ Democratic Party (HDP) -- remain opposed to the presidential system.