The first message was sent to Colchester MP Will Quince on Wednesday after he spoke out earlier this week in a row over proposed cuts to maternity services in Cumbria.
Mr Quince said he was "horrified" to receive abuse from an anonymous Twitter user called The Horse Respecter.
One message said the user was "glad his Tory baby is dead".
Later messages, using graphic language, claimed Mr Quince had "savoured" his child's agony and that "Tories enjoy disabled people suffering".
Mr Quince said: "It was horrible. To be honest, I was more worried about my wife seeing it. Despite me messaging her to say 'Don't go on social media', she saw them in the end. It was upsetting."
He added that he was "reluctant to go to the police" but after seeking advice felt it would be wrong to "just ignore these things" as it sent out "a very wrong message".
Mr Quince reported the tweets to the Metropolitan Police on Thursday.
The force said a case of malicious communication had been reported and an investigation was being carried out by the parliamentary liaison and investigation group.
Abusive social media messages about a Conservative MP's stillborn son are being investigated by police.