The answer to this question can be found in Act II scene 1 of this excellent tragedy. The conspirators are gathered together, and they are working out a list of those who need to be killed in order to ensure that their assassination of Caesar and the usurpation of power is successful. It is Cassius who suggests that Antony should not "outlive Caesar," and suggests, quite accurately as it turns out, that he would be a "shrewd contriver" who could act against them. It is thus that he argues that the conspirators should "Let Antony and Caesar fall together."
However, Brutus argues against this, saying that to kill Antony in addition to Caesar would be equivalent to cutting the head off a corpse and then hacking the limbs. He says that Mark Antony is "but a limb of Caesar" and thus once Caesar himself is killed will be harmless:
And for Mark Antony, think not of him;
For he can do no more than Caesar's arm
When Caesar's head is off.
In Act II the conspirators Cassius, Cinna, Metellus Cimber, Trebonius, Casca and Decius Brutus meet at Brutus’s house and discuss how they are going to kill Caesar. During these deliberations one of the conspirators, Decius Brutus, asks if it is only Caesar that will be killed or if there are others who should suffer the same fate. Cassius responds to Decius by stating that Mark Antony should also be killed because he has the ability to become an impediment in their plans and that he is Caesar’s good friend. Brutus objects and states that they would seem too violent and further suggests that by sacrificing Caesar they will be considered heroes but by killing Antony they become murderers.
Our course will seem too bloody, Caius Cassius,
To cut the head off and then hack the limbs,
Like wrath in death and envy afterwards;
For Antony is but a limb of Caesar:
Brutus tries to convince Cassius that Mark Antony will lose his ability to become an impediment once Caesar is dead.