If your matlab code is floating point code the must convert in to the fixed point code. because FPGA needs the fixed point code. by using the fixed-point converter MATLAB Apps, during this conversion u must focus on the fractional length and word length.these two are very important parameters.Then used HDL coder APPs on the fixed point matlab code to generate the HDL code.
see this paper
Conversion of MATLAB code in VHDL using HDL Coder & Implementation of Code on FPGA
I've only used Xilinx FPGA, so my answer will cover just Xilinx technologies:
Yes, you can convert directly. As Krishna stated, Simulink has its own HDL coder (a C coder is also available). But I believe the most appropiate tool for your question is Xilinx System Generator. Unfortunately is only included in some suites of Vivado (WebPack does not include it) and needs a specific version of MATLAB; usually a range of versions is given for it.