in your mat-cell you can get index like *ngFor as below
<mat-cell *matCellDef="let element;let i = index;">
        {{ i }}
</mat-cell>
Update from Angular 5 use also index as i
<ng-container matColumnDef="rowIndex">
  <th mat-header-cell *matHeaderCellDef> Index </th>
  <td mat-cell *matCellDef="let element;index as i;"> {{ i }} </td>
</ng-container>
index: number: The index of the current item in the iterable.  
first: boolean: True when the item is the first item in the iterable. 
last: boolean: True when the item is the last item in the iterable.  
even: boolean: True when the item has an even index in the iterable.  
odd: boolean: True when the item has an odd index in the iterable.