After tests showed he was suffering from high blood pressure, doctors sent the president back to his Brussels hotel and advised him to rest for 48 hours, a Cypriot government statement said.
Anastasiades contacted European Council President Herman Van Rompuy to let him know he would not be able to take part in a two-day summit, starting on Thursday and focusing on climate change policy and the economy.
Greek Prime Minister Antonis Samaras will represent Anastasiades, Cypriot government spokesman Nikos Christodoulides said on Twitter.