No. Your motherboard probably does not have a 2.0 slot, but that is not necessary to run the card. All PCI-E x16 2.0 devices are backwards compatible with PCI-E x16 (1.0).
To give you a definite answer, you could tell us your exact motherboard model. You can use CPU-Z
to show your system configuration and find out what type of motherboard you have exactly.