The number of financial approvals from June, the most recent number available, was 80 percent lower than the monthly average for 2016, the World Health Organization said in a statement.
Just 477 Gazans were given financial approval to travel for treatment during the month, down from 1,883 in June the previous year.
The Palestinian Authority has officially denied any change in policy, but Abbas has been seeking to squeeze Gaza's rulers Hamas through a series of measures including reducing electricity payments.
In a statement to AFP, health ministry official in Gaza Medhat Muhesan condemned the "punitive measures".
"We need international organisations to pressure Abbas's government to stop the punitive measures against Gaza," he said.
Hamas seized Gaza from Abbas's Fatah party in 2007 and the two have been at loggerheads since.
Gazans seeking medical care outside of the strip must first apply to the Palestinian Authority for permission and financial aid, before seeking Israeli permits.
Poverty is widespread in the enclave, with unemployment at some 42 per cent, while advanced medical equipment is lacking.
"The Palestinian Authority has been taking certain measures to at least slow access to proper health care," Robert Piper told AFP.
"These sorts of measures for us are not acceptable.
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