Massachusetts voters passed by a two-thirds majority Tuesday an amendment to the state constitution allowing the state to grant funds to private institutions of higher education.

The amendment, which passed with an estimated 720,626 votes, removes the present constitutional prohibition against the use of public monies for "founding, maintaining, or aiding" any college which is "not publicly owned and under the exclusive control, order and superintendence of public officers."

The new amendment also deletes a clause of Amendment 46 to the state constitution which requires that all monies raised by taxation for the support of public schools shall only be expended in schools "under the order and superintendence" of public authorities.

The deletion will allow funds raised by taxation for the support of public schools to be used in grants to private higher educational institutions.

Hale Champion, vice president for finances, said yesterday the effect of the new amendment will depend upon the criteria for granting funds adopted by the state legislature.

Champion said the "only major effect" the amendment could have on Harvard would be a possible state decision to grant funds to Harvard for extra financial aid to students who are Massachusetts residents.

Any legislation passed under the new amendment would grant aid only to Massachusetts citizens, Champion said.

He said that Harvard would be "delighted" with a grant of state funds for financial aid purposes.

Michael F. Brewer, assistant to the vice-president for government and community affairs, said the amendment enables the state legislature to consider five main options in granting aid to Massachusetts students:

* Expansion of the existing Massachusetts state scholarship program;

* Direct grants to private institutions for financial aid to Massachusetts residents;

* Contracts with private institutions whereby the state would provide scholarship funds if the college or university agrees to offer certain courses requested by the legislature;

* Institution of a state student loan program; or,

* Continuation of the present policy of granting funds only to public institutions.

Brewer said the amendment was intended to "explore other possibilities for benefiting Massachusetts students" which may be less expensive than the restriction of state funds to public institutions.

He said that aid to private colleges with unfilled enrollment capacities could enable Massachusetts students to "take advantage of existing facilities" and provide an alternative to construction of new public colleges.

Brewer said there are no bills concerning aid to private higher educational institutions now before the state legislature