It depends on which blood pressure medicine you take — grapefruit is a real problem with certain calcium-channel blockers (felodipine and nifedipine are the ones health authorities name), so don't add or stop grapefruit without checking your specific drug with your pharmacist or doctor first.
Grapefruit is not a blanket "no" for all blood pressure pills, and it's not a blanket "yes" either — the risk is drug-specific, and grapefruit can even affect different blood pressure medicines in opposite directions. With certain calcium-channel blockers, grapefruit blocks an intestinal enzyme (CYP3A4) that normally breaks the drug down, so more of it reaches your blood; the FDA specifically names nifedipine (Procardia, Adalat CC) among blood pressure drugs that interact, and MedlinePlus advises talking to your doctor about grapefruit while taking felodipine. But the FDA is explicit that grapefruit "does not affect all the drugs in the categories above," so it is not one single interaction. Some drugs go the other way: for the ARB losartan (Cozaar), the NHS says to avoid grapefruit juice "because it can stop your medicine working properly" — meaning the concern there is the medicine working less well, not too strongly. Because the exact effect hinges on your specific pill, the right move is to check the leaflet or ask your pharmacist rather than assume.
Find out your exact drug first: read the medication guide that came with your prescription, or ask your pharmacist "does grapefruit interact with THIS specific blood pressure medicine?" — the answer differs by drug. If you take an affected calcium-channel blocker such as felodipine or nifedipine with grapefruit, watch for signs the drug is running too strong: dizziness or lightheadedness, flushing, headache, a fast heartbeat, or swelling in the feet and legs; fainting, trouble breathing, or swelling of the face/lips means get emergency care. If you take losartan (or another ARB), the concern is the reverse — grapefruit may blunt the medicine, so your blood pressure could run higher than expected. Don't rely on spacing your pill and your juice a few hours apart to make it safe; the guidance for affected drugs is to check with your clinician, and never stop your blood pressure medicine on your own.
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.