The 34-year-old world number 23 is the fourth-ranked Spaniard and would have qualified for his third Games.
The Olympics, which run from 5 to 21 August, are in the middle of the North American hard-court season, building up to the US Open in September.
Lopez said his aim was to have the "best possible tournaments this summer, especially in the US".
The 2014 Queen's finalist said on his Facebook page: ""I have always felt a special pride in representing Spain in all competitions and this has therefore been a very difficult decision."
Fifty-six men and women will qualify for the singles at the Olympics based on their rankings on 6 June, with no more than four from any one country.
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Spain's Feliciano Lopez will not compete at this summer's Rio Olympics because of the demands on his schedule.