It’s generally considered bad practice. The problem is that the constants are part of the public “interface” (for want of a better word) of the implementing class. This means that the implementing class is publishing all of these values to external classes even when they are only required internally. The constants proliferate throughout the code. An example is the SwingConstants interface in Swing, which is implemented by dozens of classes that all “re-export” all of its constants (even the ones that they don’t use) as their own.
But don’t just take my word for it, Josh Bloch also says it’s bad:
The constant interface pattern is a poor use of interfaces. That a class uses some constants internally is an implementation detail. Implementing a constant interface causes this implementation detail to leak into the class’s exported API. It is of no consequence to the users of a class that the class implements a constant interface. In fact, it may even confuse them. Worse, it represents a commitment: if in a future release the class is modified so that it no longer needs to use the constants, it still must implement the interface to ensure binary compatibility. If a nonfinal class implements a constant interface, all of its subclasses will have their namespaces polluted by the constants in the interface.
An enum may be a better approach. Or you could simply put the constants as public static fields in a class that cannot be instantiated. This allows another class to access them without polluting its own API.