Facebook Inc.’s difficult year is taking a toll on employee morale, with several key measures of internal sentiment taking a sharp turn for the worse over the past year, according to people familiar with the matter and messages reviewed by The Wall Street Journal.

Amid a plunge in the stock price, ongoing leadership turmoil and critical media coverage, just over half of employees said they were optimistic about Facebook’s future, down 32 percentage points from the year earlier, according to the survey, which was taken by...