"I am very grateful for the prize, but I believe that Palestinian students should have an opportunity to go elsewhere to acquire an education," he told the newspaper.
"Students in the West Bank and Gaza today do not have an opportunity to do that."
Israel has banned most Palestinians from leaving the Gaza Strip for years.
The move has forced hundreds of Palestinian students to abandon or postpone university studies outside the small territory.
Israel's separation barrier, in many places an eight-metre-high concrete wall, has also made it even harder for Palestinians to travel across the West Bank.
Israel says "security considerations" are the reason for the travel restrictions and the barrier's construction.
Ilan Pilo, the chief executive of the Wolf Foundation, said the foundation "does not get involved in how prize winners use the money they receive".
The foundation awards prizes of up to $100,000 "to outstanding scientists and artists for achievements in the interest of mankind and friendly relations among peoples," according to its website.
The foundation presents five or six annual prizes which are often shared.
'Education for all'
The Israel-based foundation was established by Ricardo Wolf, a German-born inventor, diplomat and philanthropist who was Cuba's representative to Israel, where he died in 1981.
Mumford, who won his award for his work on algebraic theory, shared this year's award with Pierre Deligne and Phillip Griffiths, both from Institute for Advanced Study, also in the US.
The professor said he did not see himself as a political person, but was motivated by his belief that academic study should be available to all.
"Higher education, access to mathematical knowledge, is something that should be shared and should be accessible to everyone."