Yes — at normal supplement doses zinc and magnesium are commonly taken together (including in combined products) and aren't expected to interact dangerously, but stick to sensible amounts and check with your pharmacist.
The NIH Office of Dietary Supplements notes that one study found very high doses of zinc from supplements (142 mg/day) can interfere with magnesium absorption and disrupt magnesium balance in the body. That 142 mg/day is more than three times zinc's tolerable upper limit of 40 mg/day, so ordinary combined doses don't come close to the level seen in that single study, and NIH presents it only as an isolated finding rather than an established concern. At typical amounts (zinc RDA is 8–11 mg/day for adults; magnesium's upper limit from supplements is 350 mg/day), the bigger issue is not the pairing itself but taking too much of either mineral.
Keep total daily zinc at or below 40 mg unless a clinician directs otherwise — chronic high zinc (around 50 mg or more for weeks) can blunt copper absorption, lower immune function, and reduce HDL cholesterol, and acute excess causes nausea, vomiting, cramps, and headaches. Keep supplemental magnesium at or below 350 mg/day; more than that commonly causes diarrhea, nausea, and stomach cramping, and people with kidney disease can build up dangerous magnesium levels and should only use it under medical supervision. If you take antibiotics (tetracyclines/quinolones), bisphosphonates, diuretics, or proton-pump inhibitors, separate the timing and ask your pharmacist, since both minerals can affect how some drugs are absorbed. Watch for ongoing loose stools, persistent nausea, or signs of copper deficiency (fatigue, anemia, numbness), and check with a pharmacist or doctor before combining — especially if you're pregnant, have kidney problems, or take prescription medicines.
This is general reference, not medical advice, and not a guarantee of safety. Interactions depend on your doses, health conditions, and other medicines. Always confirm with your pharmacist or doctor before combining products, and follow the dosing on each label.