Full-back Murphy suffered a knee injury during last weekend's 9-9 draw against Saracens at Wembley.
But wing Benjamin, who joined Tigers from Worcester earlier this year, faces up to four months out recovering from a neck problem.
"Geordan has a bruised knee and will be (out for) three or four weeks," Cockerill told the Leicester Mercury.
"Unfortunately, Miles suffered a pretty nasty injury to his neck against Northampton in the A League two weeks ago which has resulted in a spinal injury.
"He will be potentially out for three to four months.
"The injuries are disappointing and you don't want them, but that will give opportunities for someone else to come into the side and perform."
Like Quins, Leicester are unbeaten after three Premiership games this season, with the Saracens draw following victories over London Welsh and 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.
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Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
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The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
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The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.
