I have a 40 amp breaker for the range receptacle, but the new range specifies a 50 amp circuit.
Can I just have a 50 amp breaker installed or will it require rewiring?
In general, no. Installing a 50A breaker on wiring only designed to support 40A is dangerous and can result in a house fire. 40A circuits need #8 copper wire, whereas 50A circuits need #6 copper.
It's possible, although very unlikely, that the wiring used in the circuit is #6 and thus could support 50A (maybe somebody was planning for the future), but for some reason a 40A breaker was used. The only way to know for sure is to open it up and look at the wiring. The size and other specs should be printed on the sheath; as isherwood mentioned, you're looking for AWG #8 or something similar.
In the more likely case that the existing wiring is #8, you'll either need to pull new #6 wire or get a different (lower-powered) stove that will work with the existing 40A receptacle.
Modern best-practice is to run 6 AWG cable on the stove circuit and then fit a 50A receptacle, which is legal on both 40A and 50A circuits since there is no such thing as a 40A receptacle. Then, once it is known whether the range is 40A or 50A, that correct breaker is fitted.
On the other hand, if it was known the range would be 40A, they may well have fit 8 AWG cable, which is not fit for 50A.
The wire size is written along the edge of the cable jacket, every 12 inches, along with a lot of other useless garf. This can be seen anywhere the cable is visible. On a fully finished house, that may be nowhere. In that case, you'd have to pull the wires out and measure their diameter with a micrometer or other tool.
Save yourself some money and keep the 40A breaker, as the other answers have mentioned, you're probably looking at rewiring to run a 50A circuit. Worst case, you trip the breaker if you turn on the oven and all burners to high while cooking dinner, but seriously do you ever see yourself doing that?