Abbett Elementary School is named for Merle J. Abbett, who was superintendent of Fort Wayne Community Schools from 1932 to 1952. The school was built in 1949, the first built after World War II, and was the first to be named after a superintendent still in office. The school initially housed students in grades kindergarten through eighth grade with the upper grades leaving the building as junior high schools and then middle schools opened.
Abbett is a Title I school and offers the English Language Learners program. The school participates in the Blessings in a Backpack program, which provides students with food to take home over the weekend. Students attending Abbett feed into Lane Middle School and South Side High School. The school is located in the Board of School Trustees District 4.