The data sheet "Cisco SFP Modules for Gigabit Ethernet Applications Data Sheet" says "the minimum cable distance for all SFPs listed (multimode and single-mode fiber) is 6.5 feet (2 m)."
However even though the transmit maximum power is equal to the receive maximum power, for very short distances (5m) I get receive overload warnings which may be due to reflections (see my question "1000BASE-LX/LH Receive power level greater than transmit power level" )
The datasheet text quoted in the other answer is for the "1000BASE-ZX SFP for Long-Reach Single-Mode Fibers" which have a higher transmit than receive power
The 1000BASE-LX/LH can use SM or MM, however mixed SM and MM cable in the fixed plant causes me a lot of headaches and I would recommended SM with attenuators if needed.