Low-dose pills normally lower blood pressure levels by a similar amount, researchers said.
Researcher cardiologist Dr Manolis Kallistratos at the Asklepieion General Hospital in Greece, said: "Based on our findings if someone has the luxury to take a nap during the day, it may also have benefits for high blood pressure.
"Napping can be easily adopted and typically doesn't cost anything."
The findings were based on a study of 212 people with an average age of 62 and over half were women.
The findings are due to be presented at the American College of Cardiology's annual conference in New Orleans later this month.
However, Dr Sonya Babu-Narayan, associate medical director at the British Heart Foundation, said patients should consider other lifestyle changes first.
She said: "Getting enough sleep is important for both our general wellbeing and our heart and circulatory health. But there's good evidence to show healthy lifestyle choices, such as cutting down on your salt and alcohol intake, maintaining a healthy weight and exercising regularly, are the best ways to help us keep our blood pressure low.
"As tempting as it might sound to swap all of these measures for a daily siesta, making healthy lifestyle choices remains the key to preventing heart attacks and strokes, along with taking medication where recommended."