I created a worksheet with data in cells A2:W7945, each cell containing a string with a space. I ran your code on it. It took just 7.6 seconds to complete all the cells, so if yours takes 20 minutes, it suggests that the root cause of the slowness lies elsewhere. What else are you doing in your worksheet that could be causing it? Have you tried turning off calculation while looping through the cells?
Sub Macro1()
Dim ST As Single
ST = Timer
Dim MyCell As Range
Application.Calculation = xlCalculationManual
For Each MyCell In ActiveSheet.Range("A2:W7957")
If InStr(MyCell.Value, " ") > 0 Then
MyCell.Value = Chr(34) & MyCell.Value & Chr(34)
End If
Next MyCell
Debug.Print "Elaped time for X = " & Timer - ST
Application.Calculation = xlCalculationAutomatic
ActiveWorkbook.SaveAs FileName:="C:\Cartel1.csv", FileFormat:=xlCSVUTF8, CreateBackup:=False
End Sub