Ridding oneself of living creatures could involve the melachot[1] of tzad (trapping) and/or shochet (killing). If one does either of these in order to prevent personal harm, not to get benefit from the animal, then it is a melacha she’eina tzericha legufa, a melacha not done for a classic positive outcome. We pasken that melacha she’eina tzericha legufa is prohibited only rabbinically. Regarding the trapping of some creatures, including mosquitoes, there is an additional point of leniency. Trapping creatures belonging to a species that, as a rule, is not hunted for use is also only rabbinically prohibited.[2] If one has reason to fear that the animal is about to bite him, he may remove it by hand, which includes trapping, to avoid pain.[3] However, since it is halachically worse to kill these creatures than to trap them, killing is not permitted unless there is a strong danger of more significant pain.[4] Thus, mosquitoes, which usually cause discomfort but not significant pain, should, in most circumstances, not be killed on Shabbat.
A few significant exceptions exist. One who has a specific allergy or sensitivity to mosquito bites may kill them to prevent being bitten. It would seem, in our unprofessional estimation, that applying a repellent (application by stick must be done before Shabbat) and/or spraying the immediate area are more effective and halachically preferable types of prevention.[5] Another exception exists when an infestation is likely to bring about multiple bites, which, cumulatively, can cause significant pain. However, in many cases, it is questionable whether killing a few mosquitoes before going to bed would make a substantial difference.
In areas affected by malaria or West Nile Disease, a determination may be made that there is a safek pikuach nefesh (possibility of mortal danger). If so, anyone would be allowed to take various necessary steps, including killing mosquitoes. This determination should be made by a competent posek, in consultation with health authorities.