The NFC West champions also promoted rookie linebacker Trevon Young from the practice squad to the active roster Tuesday.
Brown injured his collarbone earlier this month. He has spent four seasons as Todd Gurley’s backup, racking up 264 yards from scrimmage this year.
Hatfield will need surgery after injuring his ankle Sunday. The Los Angeles native played extensively on special teams during his second season with the Rams.
Young was a sixth-round pick out of Louisville. He has played in two games for the Rams, and he recovered a fumble against San Francisco.
The Rams (11-2) host defending Super Bowl champion Philadelphia (6-7) on Sunday night.
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