In Hamlet Act IV, scene iii, the main reason that Claudius cannot take political action against Hamlet is that the people of Denmark love him.  Hamlet is the first son of Denmark, a popular prince whom many feel deserved the crown after his father died. 

Claudius knows that imprisoning him would be political suicide on his part:

Yet must not we put the strong law on him:
He's loved of the distracted multitude,
Who like not in their judgment, but their eyes;
And where tis so, the offender's scourge is weigh'd,
But never the offence. To bear all smooth and even,
This sudden sending him away must seem
Deliberate pause: diseases desperate grown
By desperate appliance are relieved,
Or not at all.

Literally translated, this means:

Yet we must not put the strong law on him.
He's very popular with this country’s masses,
Who like not in their minds, but with their eyes,
And where it is so, the offender's punishment is
important, but never the offense. To deal with everything
smoothly and evenly, this sudden sending him away
must seem like a planned event. Diseases grown
desperate are best healed by desperate measures,
Or not at all.

Claudius says that the people value appearance over reality.  What a hypocrite!  He's saying the people only like Hamlet because he's young, blond, and hot. 

Who knew Hamlet was like an older version of Prince William? 

The main reason that Claudius gives comes right at the beginning of the scene.  He says that he cannot take legal action because the people love Hamlet too much.  If he puts Hamlet in jail, the people will be angry.

I think there are two other reasons:

• I don't imagine that Gertrude really wants Hamlet put in prison either.  So Claudius is probably doing it partly for her sake.
• Claudius is arranging to have Hamlet killed anyway.  So why bother with a trial when you can send him off and have him killed and you won't even be blamed for it?