Kerber, who made the semi-finals in 2012, was knocked out by Estonia's Kaia Kanepi, 3-6, 7-6 (8/6), 6-3 in the second round despite leading by a set and 5/1 in the second-set tie-breaker.
Her Facebook page received a string of abusive messages including a death threat as well as one wanting her to break her arms while another demanded the tie be investigated for match-fixing.
"Fat cow, burn in hell," said one message with another screamed "I wish you broken hands".
Another described her as a "fat, German cow".
"Just embarrassing Angelique. Horrible horrible performance today. Very disappointed," one of the less abusive posts.
Kerber did not address the abuse in her post-match press conference, but admitted she hadn't seized her chances to clinch the win.
"I had my chances in the second set but I didn't take them. In the third she was playing unbelievable and I couldn't do anything. I mean, she won today. Well done to her," said the German.
Angelique Kerber suffers Internet abuse after Wimbledon woe
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