The attacks took place in Jaranwala in the province of eastern Punjab.
Police said at least four churches had been set on fire, while residents said up to a dozen buildings connected to churches had been damaged.
Blasphemy is punishable by death in Pakistan.
No-one has ever been executed for it, but dozens have previously been killed by mobs after being accused of the crime.
The Muslim community is believed to make up over 96% of Pakistan's population.
Police making the case against the two Christian men say they found pages of the Quran, the holy book of Islam, with derogatory remarks written in red, Reuters reported.
Yassir Bhatti, a 31-year-old Christian, was one of those to flee their homes.
"They broke the windows, doors and took out fridges, sofas, chairs and other household items to pile them up in front of the Church to be burnt," he told AFP news agency.
"They also burnt and desecrated Bibles, they were ruthless."
Videos uploaded to social media show protesters destroying Christian buildings while police appear to watch on.
Amir Mir, the information minister for Punjab province, condemned the alleged blasphemy and said in a statement that thousands of police had been sent to the area and dozens of people had been detained.
The mob was mostly made up of people from an Islamist political party called Tehreek-e-Labbaik Pakistan (TLP), a government source told Reuters. The TLP has denied any involvement.
Caretaker PM Anwar ul Haq Kakar called for swift action against those responsible for the violence.
Pakistani bishop Azad Marshall, in the neighbouring city of Lahore, said the Christian community was "deeply pained and distressed" by the events.
"We cry out for justice and action from law enforcement and those who dispense justice, and the safety of all citizens to intervene immediately and assure us that our lives are valuable in our own homeland," he posted on X, formerly known as Twitter.
By George Wright