The 27-year-old Argentinian was given the ban at a Rugby Football Union disciplinary hearing at the Bristol Filton Holiday Inn on Tuesday night.
Camacho had been cited for a dangerous tackle on Grove during the Aviva Premiership match at Sixways on April 14.
The panel, chaired by Rick Charles with John Doubleday and Dan White, amended the charge and the player was charged and found guilty of a pick-up, tip-tackle.
Camacho, who pleaded guilty, can return to action on May 16.
Exeter are currently fifth in the Premiership, one place and one point behind Northampton following their home defeat to the Saints on Sunday.
Rob Baxter's men tackle Saracens at Vicarage Road in the final round of league action on May 5 while Northampton host Worcester.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
$29.99
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.
