Will an intramuscular injection cause sciatica if it is given in the wrong location on the buttocks?

Yes: It can if it is injected too low and too medially.

Sciatica: To be specific, sciatica is usually the common term for lumbar radiculopathy. This is a disease in which spine arthritis causes pinching of spinal nerves at the level of the spine with lower extremity pain and numbness. An injection into the buttocks does carry the risk of directly injecting the sciatic nerve causing a peripheral nerve injury. Same name but different treatment.

Its possible: If the injection was not given on the upper outside area of the buttock. Occasionally though the injection site can irritate the muscle around the sciatic nerve and cause pain. If it does not resolve, I would consider getting an evaluation for this.