Usually yes — oral magnesium supplements are commonly taken alongside blood pressure medicine and the NIH does not flag a dangerous direct interaction, but stay at or below 350 mg/day from supplements, be careful if you have kidney problems, and clear it with your doctor or pharmacist first.
The NIH Office of Dietary Supplements lists magnesium's notable drug interactions as oral bisphosphonates and certain antibiotics (tetracyclines and quinolones, an absorption issue), diuretics (loop and thiazide diuretics deplete magnesium, while potassium-sparing diuretics reduce its excretion), and long-term proton-pump-inhibitor acid-reflux drugs — it does not name common blood pressure pills (ACE inhibitors, ARBs, calcium channel blockers) as a hazardous combination by mouth. Magnesium supplements do lower blood pressure, but only by a small amount (the NIH cites roughly 2–4 mmHg in trials), so the added effect on top of medication is modest. The main cautions the NIH does flag are that the kidneys clear excess magnesium, so people with impaired kidney function or kidney failure can build up toxic levels, and that very high intakes can themselves cause low blood pressure (hypotension), irregular heartbeat, and difficulty breathing. The NIH sets the Tolerable Upper Intake Level for supplemental magnesium at 350 mg/day for adults (magnesium from food and beverages is not capped).
Keep supplemental magnesium at or below the adult upper limit of 350 mg per day unless a clinician directs otherwise (magnesium from food is not capped; the UK NHS uses a similar threshold, calling 400 mg/day or less from supplements unlikely to cause harm). Avoid magnesium supplements, or use them only under medical supervision, if you have kidney disease or reduced kidney function, since excess can build up to toxic levels. If you take a diuretic ("water pill"), your magnesium can run low (loop and thiazide types) or high (potassium-sparing types), so your doctor may want to check your levels. Watch for signs of too much magnesium: diarrhea, nausea and cramping at high oral doses, and — at extreme levels — dizziness or fainting from low blood pressure, irregular heartbeat, or trouble breathing; seek care if these occur. To avoid absorption problems, separate magnesium from oral bisphosphonates and certain antibiotics (tetracyclines, quinolones) by at least 2 hours. Tell your doctor, pharmacist, and other healthcare providers about every supplement and medicine you take so they can check your specific drugs and kidney status before you start.
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.