The foreign ministry advised Iranian pilgrims "intending to travel to Iraq to delay their journeys until conditions ease in the country".
Iranians take part in large numbers in the annual pilgrimage to Imam Hussein's tomb in Karbala, 110 kilometres (68 miles) south of Baghdad, that culminates on October 17 with Arbaeen commemorations.
On Wednesday, Iranian state television announced that one of the three border posts used by pilgrims to enter Iraq had been closed "at the request of Iraqi authorities".
In 2018, around 1.8 million Iranians took part in the Arbaeen pilgrimage, according to official figures.
Iraq on Tuesday saw the eruption of mass rallies against corruption, unemployment and poor public services.
The protests have escalated with thousands of demonstrators clashing with security forces in Baghdad and across mainly Shiite southern Iraq, leaving more than 30 people dead.