Answer
The distance from the wire should be short compared to the wire’s length.
Work Step by Step
If we are calculating the magnetic field at a point that is “very close” to a current-carrying straight wire (the distance from the wire is to be compared to the wire’s length), then we may consider the wire to be infinitely long. For example, if the point is 1 mm away from the middle of a 10-m long wire, almost no error is introduced by ignoring the segments of wire that are more than 5 m away.