Swiatek recently spoke out about the emotional toil she has faced in recent months, having served a one-month ban for a doping offence and not wanting to “step on the court”.
Since the incident at the weekend, the second seed has gone on to reach the Miami Open quarter-finals, where she faces Filipino teenager Alexandra Eala on Wednesday.
“Security is a top priority. We monitor the network to catch these types of issues,” her spokesperson said.
“Constructive criticism is one thing, and threats, hate speech or even disturbance during training is another – this cannot be condoned.”
Tournament organisers and the WTA are said to have reacted quickly, putting extra security measures in place around the former long-time world number one.
Miami Open organisers told AFP the safety and security of everyone at the tournament is treated “extremely seriously”.
“We constantly evaluate any potential threats and take every measure to respond appropriately,” they said.
BBC Sport has contacted the WTA and Miami Police for further comment.
Swiatek’s experience is the latest incident involving a WTA player, providing a stark reminder of the dangers faced by female athletes on a regular basis.
Raducanu, 22, recoiled in horror when she saw a man – who she had already reported for what was described as “exhibiting fixated behaviour” – in the stands of her match in Dubai last month.
Stephanie Hilborne, the chief executive of the Women in Sport charity, told BBC Sport that “every single woman has a level of fear”.
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