The church is at 200 Pettaconsett Ave. in the Norwood section of the city.
Parishioners were informed over the weekend, during Mass.
The final Mass is scheduled for Easter Sunday.
The statement said St. William had 513 registered families in 2016, down from 854 in 2013.
There have been no baptisms in 2017 and there were just three in all of 2016.
The statement added that the church has accounts payable estimated at $203,000 and parish reserves totaling $12,700.
Projections indicate that the parish will be out of money by the end of this month.
"The closing of a church is always a moment of sadness, but also an opportunity for renewed prayer and reflection," said Bishop Thomas J. Tobin. "I am most grateful for all those who have supported the parish, personally and financially, over the years, as well as to the pastors who have provided dedicated leadership. Fortunately, the parishioners of St. William's have several other outstanding churches in the area where their spiritual needs will be adequately met."
When reached for comment, a woman at the church referred question to the parish administrator, the Rev. Frank Salmani. Father Salmani could not be reached for comment on Monday.
But the church's website outlines recent struggles the parish faced. A listing of events included a "town hall" meeting in January "to discuss the future of the parish."
A later update announced the final Mass on Easter and that "budget envelopes will be distributed through April. We still need to pay salaries and utility bills, so your generosity will be greatly appreciated."
In 2008, the parish celebrated 75 years, according to the church's website.
St. William Church was a mission of the St. Matthew Church in Cranston.
The original church building was near Harrington, Perry and Majestic avenues and was dedicated as a chapel in 1926.
Then in 1933, it became a parish.
Six acres were purchased in 1958 as the parish grew, and the new building was dedicated in 1960.
There are nine other Catholic parishes in Warwick, according to the diocese website.