What is the Christian Form of Government?

I was once asked about what form of government that the Bible prescribes.
Islam has the concept of sharia law, so is there an equivalent concept in Christianity?

Actually, Christianity does not have a concept of a government that is comparable to what Muslims have.

Jesus said, "my kingdom is not of this world" (John 18:36).  He was not establishing a form of government.

Paul writes about government,

...he beareth not the sword in vain: for he is the minister of God, a revenger to execute wrath upon him that doeth evil.
--Romans 13:4

Here the Government has the sword, not the church. The symbol for Christianity is the cross, but the symbol of Islam is the sword, specifically a Scimitar  (a  cured sword).  See the Wiki page.

What Christianity offers in place a form of government is the Kingdom of God.  The first words of Jesus in Mark's gospel are about this:

14 Now after that John was put in prison, Jesus came into Galilee, preaching the gospel of the kingdom of God,
15 And saying, The time is fulfilled, and the kingdom of God is at hand: repent ye, and believe the gospel.
--Mark 1

Where is the kingdom of God?  It is where ever people are obedient to God.  When Adam and Eve ate the fruit that was forbidden, they rebelled against the rule of God over them.

 The ultimate expression of this rebellion is described in 2 Thessalonians 2:3 with  "the man of lawlessness" (NASB).

However, God offers you the opportunity to be restored to fellowship if you repent and submit to his authority if you repent and believe the Gospel.  This is government directly from God, not from man.