About 30 witnesses are expected to testify at hearings at the state Department of Environmental Conservation in Albany.
The DEC estimates that Indian Point's system for withdrawing and discharging water from the Hudson River kills more than 1 billion fish, eggs and larvae every year.
The hearings will address proposals to shut the plant for 42 to 92 days each summer when fish are spawning.
"We look forward to providing the court with sensible alternatives to the destruction of a shocking percentage of Hudson River fish," Cristopher Len, Hudson program director for the environmental group Riverkeeper, said in a statement.
Riverkeeper says several species including American shad, river herring and white perch are vanishing from the Hudson and should be protected.
Entergy Corp., which operates the nuclear plant in Buchanan, about 30 miles north of Manhattan, disputes the fish mortality numbers.
"Entergy continues to advocate that Indian Point right now is fully protective of life in the Hudson River, and $75 million spent over 30 years on scientific study demonstrates that the facility has no harmful impact on adult fish populations," Entergy spokesman Jerry Nappi said.
Nappi said written testimony submitted by the DEC's own expert witnesses indicated that summertime closures at Indian Point would lead to higher electricity costs for consumers.
He said the annual shutdowns would also affect air quality adversely by forcing greater reliance on fossil fuels.
The hearings are expected to last up to three weeks.