You can use a 'traditional' PivotTable to do this. See ashleedawg's great answer. 
You can also use a 'OLAP' PivotTable that's based off something called the Data Model to do it, that has a small advantage over the 'traditional' PivotTable in that you don't need to clear the PageFilter after refreshing. (More on this at the bottom of my answer). 
Any Excel version from Excel 2013 later has the DataModel built in by default, and you also get access to the DataModel in 2010 if you install Microsoft's free PowerPivot add-in. Using the DataModel, here's what you need to do:
Turn your data into an Excel Table using the Ctrl + T keyboard shortcut:

Make a PivotTable out of it, but be sure to check the Add this data to the Data Model option: 

Add Group to the Rows pane of the PivotTable, then right-click on Table1 in the fields pane and select Add Measure...:

Give the new Measure a name (I've called it Min Without Zero) and type =CALCULATE(MIN(Table1[Price]),Table1[Price]>0) in the Formula box then push OK:

Put a tick in the Min Without Zero checkbox in the PivotTable fields list.

Bing! The PivotTable shows the min (excluding zero) of each group by price.
Edit: I'd probably use ashleedawg's answer if I was doing this myself. But there's one caveat: If you add additional data in future and refresh, then you need to clear the filter and reapply the zero exclusion to be absolutely sure that any new numbers in the data are included. By way of a demonstration, if I filter out zero from a PageField, then I get just the result I expect:

...and here's how the filter looks:

But if I add new data and refresh, note that nothing has changed in the PivotTable:

...and if I look at the filter I can see why:

That's because when you deselect something from a filter, you're not actually saying "Give me everything except this thing" but rather "Give me the other things currently visible in this list, but leave any new things unselected."
Easily enough fixed: Just clear the filter and deselect zero again (or write some VBA code to do it automatically on refresh). 
Minifsis not a normal excel formula. Are you having some VBA function named that? If yes, we will need to look at its code - Raunak Thomas