Christian Solidarity Worldwide (CSW) organised the demonstration after revealing that there are at least 1,500 Christians imprisoned "in truly inhumane conditions".
The "Free Eritrea" vigil at the building in central London will call for the country to start respecting human rights and the freedom of belief.
Mervyn Thomas from Christian Solidarity Worldwide told Premier torture is rife in prisons there.
He said: "Eritrea is one of the worst countries in the world for religious freedom and for human rights actually.
"It was in May 2002, 13 years ago now, that they started putting Christians and Christian leaders in prison."
He added that there were between two and three thousand Christians being held in "the most appalling conditions".
Some prisoners were held in metal containers or underground cells, he added.
CSW said there were credible reports of female Christian prisoners being beaten on the soles of their feet and their wombs, allegedly to prevent them from bearing children.
Reports also persist of prisoners dying after torture, or after being denied life-saving medication for refusing to deny their faith.