The exobiology department was one of the science departments found aboard Federation starships during the 24th century that specialized in the studies of exobiology. During the 23rd century, this department was identified under the moniker astrobiology.
Following the arrival of the USS Enterprise to the planet Arret in 2268, several crewmembers were "summoned" to join the landing party, including Doctor Ann Mulhall, an operations division officer assigned to Astrobiology. (TOS: "Return to Tomorrow")
When Edward Jellico captained the USS Enterprise-D that year, he ordered to take the secondary distribution grid offline to increase warp coil efficiency. Chief Engineer Geordi La Forge protested the move, explaining that that would shut down the exobiology department, the astrophysics lab and geological research. (TNG: "Chain of Command, Part I")
During a briefing given to Commander Riker, during the morning shift change on the bridge of the Enterprise-D, Lieutenant Commander Data reported that during the previous shift, "Sickbay reported one minor injury in the exobiology department at 0420 hours." (TNG: "Rightful Heir")