"A total of 31 persons lost their lives in the stampede."
Images posted on social media and verified by AFP showed families crying and attending to injured people, including many children, outside the city's military hospital.
Police said a criminal investigation was underway.
National Emergency Management Agency southern region coordinator Godwin Tepikor told AFP that church members had been seated inside when the crowd of people rushed in.
"A huge crowd from outside surged into the club through a narrow gate, resulting in the stampede," he said.
"The injured and the dead have been evacuated to the hospital and mortuary."
Representatives of the church could not immediately be contacted for comment.
Nigeria has seen several stampede tragedies over food distribution in recent years, including an aid agency food programme in north Borno State where seven women were trampled to death last year.
Saturday's early morning disaster happened as the opposition People's Democratic Party leaders were gathering in the federal capital Abuja to select their candidate for the 2023 presidential race, with Rivers State governor Ezenwo Nyesom Wike among the hopefuls.
Port Harcourt is the main oil hub in Nigeria, Africa's most populous country and the continent's largest petroleum producer.
Despite its oil wealth, as many as four out of 10 Nigerians live below the national poverty level, according to a recent World Bank Report.
The Ukraine crisis has also pushed up the cost of food and fuel across the continent as wheat and gas supplies are impacted, with aid agencies warning about worsening food insecurity in Africa.