A full Moon can occur on Easter Sunday.

The rule for finding the date of Easter is usually stated as follows:

1. Determine the date of first full Moon on or after the first day of Spring.
2. Easter is the Sunday after that.

This eliminates the possibility of the Moon being full on Easter Sunday.

Except that it doesn't. A lunar eclipse can occur only when the Moon is full, and there was a nearly total lunar eclipse which was seen in most of Europe on Easter Sunday, April 12, 1903 (pdf).

There are two factors in the rule for Easter that contribute to this situation.

1. The first day of Spring is always assumed to be March 21. This is not exactly true. The vernal equinox (determined astronomically) can occur on March 19, 20 or 21.
2. The full Moon used is not the astronomical full Moon, but an ecclesiastical full Moon, i.e., one that is used for ease of determination.

The second factor is responsible for 1903, because the ecclesiastical full moon was on April 11.

The date of Easter is actually determined by the Roman Catholic Church using tables that were set up when the Gregorian Calendar was established in 1582.

For further information: United States Naval Observatory, The Date of Easter.