Here's a crude one from my Personal Workbook that I coded up.  You can
try it and/or improve it:

SteveM

Public Function MinIf(Ref_Range As Range, Criterion As Variant,
Min_Range As Range) As Single
       Dim cell As Range
       Dim minVal As Single
       Dim iRow As Integer, jCol As Integer, iCount As Integer,
jCount As Integer

       iCount = Ref_Range.Rows.Count
       jCount = Ref_Range.Columns.Count

       minVal = Application.WorksheetFunction.Max(Min_Range)

       For iRow = 1 To iCount
           For jCol = 1 To jCount
               If Ref_Range.Cells(iRow, jCol).Value = Criterion Then
                   If Min_Range.Cells(iRow, jCol).Value < minVal Then
                       minVal = Min_Range.Cells(iRow, jCol).Value
                   End If
               End If
           Next
       Next

       MinIf = minVal

End Function