Format: 

Director, A. A. (Director). (Date of performance). Title of play. Live performance at Theater, Location.

Examples: 

Meath-Lang, B. (Director). (2006, February 17). The crucible. Live performance at Robert F. Panara Theatre, Rochester, NY.

In-text: (Meath-Lang, 2006)

Source:

This source type is not covered by the APA style guidelines.
Example(s) adapted from:
APA 7.04