Doctors should think about the risks and benefits to patients taking it over many months, the University of Edinburgh researchers say.
Taking the painkiller for headaches and fevers is safe, they stress.
Other experts say research in more people over a longer timeframe is needed to confirm the findings.
Paracetamol is widely used around the world as a short-term remedy for aches and pains but also prescribed to manage chronic pain, despite little evidence of its benefit for long-term use.
Half a million people - one out of every 10 - in Scotland were prescribed the painkiller in 2018.
High blood pressure affects one out of every three people in the UK.
The study tracked 110 volunteers, two-thirds of whom were taking drugs for high blood pressure, or hypertension.
In a randomised trial, they were asked to take 1g of paracetamol four times a day for two weeks - a common dose for patients with chronic pain - and then dummy pills, or placebo, for another two weeks.
The trial showed paracetamol increased blood pressure, "one of the most important risk factors for heart attacks and strokes" much more than a placebo, Edinburgh clinical pharmacologist Prof James Dear said.
The researchers advise doctors to start patients with chronic pain on as low a dose of paracetamol as possible and keep a close eye on those with high blood pressure and at risk of heart disease.
Lead investigator Dr Iain MacIntyre, clinical pharmacology consultant, at NHS Lothian, said: "This is not about short-term use of paracetamol for headaches or fever, which is, of course, fine."