The South Africa international – who can operate at full back, wing or centre – joined the Dragons in the summer of 2017 from Leinster and has made 13 appearances in all competitions for the Men of Gwent.
Head Coach Bernard Jackman said: “We are very lucky to have a great relationship with Bristol and Pat Lam and the opportunity for Zane to go into their environment and get some game time is a positive solution for all parties.
“We look forward to seeing how Zane goes in the English competition and wish him well during his time with the Bears.”
34-year-old Kirchner joins Bristol as injury cover for Charles Piutau (shoulder) Luke Daniels (hamstring) and Matt Protheroe (knee).
“With three of our first team full-backs recovering from injury, it was important to add a player of Zane’s ability and international experience on a short-term basis as we prepare for the tough challenges ahead,” said Bristol Head Coach Pat Lam.
“Zane has played for some of the top clubs in world rugby and will slot in quickly. We’re grateful to Bernard Jackman and Dragons for their co-operation in the process.”