The incident comes as the fighting between the Arakan Army and Myanmar's military has been escalating since last week in Minbya Township, east of Sittwe, the capital of Rakhine State.
"The artillery hit the monastery where hundreds of people are taking shelter," said Ko Maung Thar Nu, who helps refugees in Minbya.
According to the abbot of the monastery, four people were killed on the spot, another three died in hospital and eight people were seriously injured, Efe news reported.
Hundreds of people have been fleeing their homes in villages to Minbya city where they believe they will be safer.
Both the Myanmar armed forces and the rebels denied responsibility, while the fighting continues in the area.
More than 33,000 people have been displaced due to the conflict between Myanmar's military and the Arakan Army since the end of 2018, according to the UN.
The Arakan Army, formed in 2009 by a handful of ethnic Rakhine nationalist students and which currently has some 7,000 fighters, is one of several armed rebel groups in the southeast Asian country.
The Rakhine ethnic group is Buddhist and forms the majority in Rakhine State, where Rohingya Muslims also live. Myanmar authorities deny citizenship to Rohingyas and classify them as "Bengali immigrants".
More than 723,000 Rohingyas fled Rakhine state to neighbouring Bangladesh following a military campaign in August 2017 by Myanmar's Army, which has been accused of genocide and ethnic cleansing by the UN.
( With inputs from IANS )