Assistant manager Wayne Carlisle and first-team coach Dave Horseman will take interim responsibility for all football duties.
The length of Taylor's absence is unclear at present however the club have asked the public to respect his family's privacy in what they describe as a 'difficult period'.
An official club statement read: "Bristol Rovers can confirm that first-team manager Matt Taylor is to take a leave of absence due to an ongoing family emergency.
"David Horseman and Wayne Carlisle will take interim responsibility for all footballing duties.
"The thoughts and prayers of everyone at Bristol Rovers are with Matt and his family during this difficult period, and we look forward to welcoming him back to work as soon as is suitable.
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"The club will be making no further comment and asks that the privacy of Matt and his family are respected during this time."
Bristol Rovers travel to Barnsley in the FA Cup second round on Saturday followed by League One matches at Leyton Orient and at home to Bolton Wanderers over the next week.
Taylor was appointed Rovers boss 12 months ago on a three-and-a-half year contract, succeeding Joey Barton.
The former Exeter and Rotherham boss made an immediate impact at the Memorial Stadium with impressive wins over promotion hopefuls Bolton and Portsmouth.
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He led the club to a comfortable 15th-placed finish last season whilst Rovers currently sit 14th in League One this season having picked up 21 points from 17 games.
The former centre-back enjoyed a 16-year playing career in the lower divisions having lined up for 14 different clubs including Exeter, Charlton Athletic and Cheltenham Town.