Update: Google's Project Zero disclosed details about the vulnerability a week ahead of schedule due to growing concerns, and they indeed confirm AMD and ARM processors are also affected:
The Project Zero researcher, Jann Horn, demonstrated that malicious actors could take advantage of speculative execution to read system memory that should have been inaccessible. For example, an unauthorized party may read sensitive information in the system’s memory such as passwords, encryption keys, or sensitive information open in applications. Testing also showed that an attack running on one virtual machine was able to access the physical memory of the host machine, and through that, gain read-access to the memory of a different virtual machine on the same host.
These vulnerabilities affect many CPUs, including those from AMD, ARM, and Intel, as well as the devices and operating systems running them.
Intel just published a PR statement about the processor flaw, and in it, it basically throws AMD and ARM under the bus. According to Intel, reports that only its own processors are affected are inaccurate, namedropping specifically AMD and ARM just to make it very clear who we're talking about here. From the statement:
Recent reports that these exploits are caused by a "bug" or a "flaw" and are unique to Intel products are incorrect. Based on the analysis to date, many types of computing devices - with many different vendors' processors and operating systems - are susceptible to these exploits.
Intel is committed to product and customer security and is working closely with many other technology companies, including AMD, ARM Holdings and several operating system vendors, to develop an industry-wide approach to resolve this issue promptly and constructively. Intel has begun providing software and firmware updates to mitigate these exploits. Contrary to some reports, any performance impacts are workload-dependent, and, for the average computer user, should not be significant and will be mitigated over time.
More to surely come.