Swansea magistrates said Robert Riley's online messages were also racially and religiously aggravated and that only a custodial sentence could be imposed.
Riley, from Port Talbot, was sentenced to eight weeks in custody after admitting posting an abusive Twitter message about the death of Leeds schoolteacher Ann Maguire.
The 42-year-old was the second person to be charged with the offence in the wake of the death of Mrs Maguire, who was stabbed to death in her classroom at Corpus Christi Catholic College last month.
Yesterday a third person was arrested in Cardiff and bailed.
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A grieving mother broke down in tears as she recalled how doctors could not find out what was wrong with her son in the run-up to his death.
Carol Morse claimed her 12-year-old son Ryan dropped to just four stone but doctors failed to act, Cardiff Crown Court hears.
Mark Prosser stabbed Billy Moore - a friend who had previously saved his life.