Trump has also been after signing the so-called "Abraham Accords" in his final months at the White House.
As part of twin deals in August, the United Arab Emirates and Bahrain became the first Gulf nations to recognize Israel as a state and establish formal diplomatic ties.
In return, Israel agreed to delay its controversial plan to annex part of the occupied West Bank.
Similar deals with Sudan and Morocco were signed in October and December.
Before then, Egypt and Jordan were the only Arab League nations to recognize Israel.
Kushner, who is married to , and Avi Berkowitz, Trump's Middle East envoy, were key figures in negotiating the historic deals.
They were nominated for the peace prize by attorney Alan Dershowitz, who is eligible to do so as professor emeritus of Harvard Law School.
Dershowitz, who in his sex trafficking case, is a Trump ally who .
In his letter to the Nobel committee, he appeared to acknowledge the nomination would be controversial.
“The Nobel Peace Prize is not for popularity" Dershowitz wrote.
“Nor is it an assessment of what the international community may think of those who helped bring about peace.
“It is an award for fulfilling the daunting criteria set out by Alfred Nobel in his will.”
Kushner said in a statement he was honored to be nominated for the prize, which will be awarded in October.
In August, Trump hailed the Abraham Accords as .
Israeli PM Benjamin Netanyahu said: "This day is a pivot of history, it heralds a new dawn of peace."
The deal was a key foreign policy victory for Trump during the election campaign, and for Netanyahu, who faces corruption charges at home.
Palestinian groups were not involved in talks, and said they had been "betrayed" by their Arab allies.
The deal smashed apart a previous pact by Arab nations to keep Israel in diplomatic isolation until it ended its occupation of the West Bank.
Critics also said the Gulf monarchies already had informal cooperation with Israel as they are united against their common enemy Iran.
None of the countries involved have ever been at war with Israel, so they are not technically peace treaties.
Joe Biden’s administration is expected to review all national security deals struck during the Trump administration, including arms packages for the UAE and Saudi Arabia.
Some lawmakers have complained about the Morocco deal because the United States recognized its sovereignty over the disputed Western Sahara.