Muguruza lost in the semifinals here previous year but at least gained four useful warmup matches before Wimbledon.
After dropping the first set, she led 4-2 in the second before collapsing and losing the last four games.
Muguruza sometimes looked languid in responding to the challenge of a feisty and hard-working Czech opponent, and occasionally became irritated by the hard windy conditions during her 6-2, 6-4 loss to Strycova. "I wish I could play more matches, but nothing really worries me".
There was no problems for defending champion Petra Kvitova, who cruised to a 6-2 6-2 victory over Australia's Daria Gavrilova.
Strycova beat the top-seeded Spaniard, 6-4, 6-4, in one hour, 26 minutes. When it was deuce, I played the second serve, she went for it, but she missed it. I think her style of game suits very good the surface.
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Muguruza started the match with an opening hold of some confidence, but the set took a downward turn for her very quickly as she tried to tackle the gusts of wind and tried to deal with the difference in spins and pace coming from the Strycova racquet.
The two-time former Wimbledon champion said: "I always feel happiness when I'm playing on the grass".
Gavrilova won their last two matchups being persistent and mobile enough to contain Kvitova's uncompromising hitting.
"My serve was a very big key today and it helped me a lot in the big moments".
Kvitova, who has won four WTA titles in 2018 - more than any other player - played some powerful backhands but served five double faults. "I like it. But I don't know why we play good on grass".
She faces fifth seed Julia Goerges in the last eight after the German halted Ashleigh Barty's strong run.