Let's say you have created a Pivot Chart and the axis labels are dates as below screen shot shown, you can easily filter the Pivot Chart by month as follows:

Step 1: Click the Date filed button in the Pivot Chart, and then select the Date Filters > All Dates In the Period and then select a month, such as January.

Note: In Excel 2007, the filed buttons are not displaying in Pivot Chart, but there is a PivotChart Filter Pane for filtering. Click the Pivot Chart, go to the PivotChart Filter Pane's Axis Fields (Categories) section (or Legend Fields (Series) section), click the arrow besides the Date, and then click Date Filters > All Dates in the Period > January or other month.

Now only data points occurred in selected month are filtered out. See below screen shot:

In some cases, you may create a Pivot Chart and the axis labels or legends are not dates as below screen shot shown. Now if you have to filter the Pivot Chart by month, you can do as follows:

Step 1: In the Pivot Chart Fields pane, drag the Date filed from Choose fields to add to report section to the Axis (Categories) section or Legend (Series) section.

Note: You can also right click the Date filed in the Choose fields to add to report section, and select Add to Axis Fields (Categories) or Add to Legend Fields (Series) from right-clicking menu.

Then the Date filed button has been added to the Pivot Chart, and you can follow the same way to filter the Pivot Chart by month.

After filtering by month, the Pivot Chart may show as below screen shot: