PACT, which works in almost 60 prisons across the UK, said staff cuts and rising inmate levels were partly to blame for what its chief executive described as a "absolute crisis".
Speaking on Premier's News Hour, Andy Keen-Downs said: "You have a situation where prisoners are often locked up for 23 hours a day."
He said the situation was affecting the ability to minister to prisoners and spread the Gospel behind bars: "Simply getting guys and women out of their cells and into a room where we can work with them is a massive, massive problem because they aren't enough officers to even unlock them."
New Ministry of Justice figures show there were 119 apparently self-inflicted deaths behind bars in England and Wales, double the figure of 2012.
They also show there were more than 25,000 assaults in the twelve months to September last year, a rise of 31 per cent compared to the previous year.
Justice Secretary Liz Truss said she has been clear that "the violence, self-harm and deaths in our prisons are too high", adding she had taken "immediate action" to make them safer.
She said: "I have taken immediate action to stabilise the estate by tackling the drugs, drones and phones that undermine security. We are also investing £100m annually to boost the frontline by 2,500 officers."
Asked whether Christians are doing enough to reach out to prisoners, Andy Keen-Downs said: "Faith is really alive and well and kicking in the prison system.
"There's a lot being done already; faith is very powerful in prisons and, for many prisoners, many come to faith or rediscover their faith in prison.
"The key, then, is to make sure that they are well received and welcomed by the Christian community; that's not always the case."
Click here to listen to Andy Keen-Downs speaking with Premier's Aaron James: