Jahic has agreed a contract until the first week in January after impressing during a 10-day trial stint with the Perth club.
The 31-year-old French-born defender was expected to provide cover for Steven Anderson after he was ruled out for the next six weeks with a dislocated thumb.
But Wright has now been handed an extra two-game suspension on top of the one-match ban he received after being sent-off in Saturday's 4-3 defeat to St Mirren in Paisley.
The former Kilmarnock centre-half was dismissed for a last-man tangle with the Buddies' Paul McGowan but ended up in even hotter water when he mouthed off at fourth official John Beaton on his way off the St Mirren Park pitch.
A statement on the St Johnstone website said: "The SFA advised the club that Frazer Wright has been banned for two games on top of his automatic one-game suspension for his red card at St Mirren.
"The defender was reported by referee William Collum for comments made to fourth official John Beaton as he left the pitch following his red card and those comments were deemed sufficient for a second red card to be issued.
"Under the SFA's procedures, an additional one match ban is awarded for each red card in a season and so Frazer misses three games v Motherwell, Hearts and Kilmarnock."